The case of the plane and conveyor belt

Here’s the original problem essentially as it was posed to us: “A plane is standing on a runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction). Can the plane take off?”

I’ll give you a few moments to think about that before discussing the answer…

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Cecil says that the obvious answer — that the plane does not take off because it remains stationary relative to the ground and the air — is wrong. The plane, he says, can take off:

But of course cars and planes don’t work the same way. A car’s wheels are its means of propulsion—they push the road backwards (relatively speaking), and the car moves forward. In contrast, a plane’s wheels aren’t motorized; their purpose is to reduce friction during takeoff (and add it, by braking, when landing). What gets a plane moving are its propellers or jet turbines, which shove the air backward and thereby impel the plane forward. What the wheels, conveyor belt, etc, are up to is largely irrelevant. Let me repeat: Once the pilot fires up the engines, the plane moves forward at pretty much the usual speed relative to the ground—and more importantly the air—regardless of how fast the conveyor belt is moving backward. This generates lift on the wings, and the plane takes off. All the conveyor belt does is, as you correctly conclude, make the plane’s wheels spin madly.

After reading the question this morning and discussing it with Meg for, oh, about 3 hours on and off, I was convinced that Cecil was wrong. There’s no way that plane could take off. The conveyor belt keeps pace with the speed of the plane, which means the plane remains stationary from the POV of an observer on the ground, and therefore cannot lift off.

Then I read Cecil’s answer again this evening and I’ve changed my mind; I’m fairly certain he’s right. For a sufficiently long conveyor belt, that plane is taking off. It doesn’t matter what the conveyor belt is doing because the airplane’s energy is acting on the air, not the belt. I had better luck simplifying the problem like so: imagine instead of a plane, you’ve got a rocket with wheels sitting on that belt. When that rocket fires, it’s eventually going to rocket off the end of that belt…which means that it doesn’t remain stationary to the ground and if it had wings, it would fly.

Update: Well, that got out of control in a hurry…almost 300 comments in about 16 hours. I had to delete a bunch of trolling comments and it’s not productive to keep going, so I closed it. Thanks for the, er, discussion and remember, the plane takes off. :)

Reader comments

The plane gets its lift via the bernoulli effect. This has to do with wing shape and its interaction with air moving rapidly past. If the plane has no motion relative to the wind, there will bo no lift to force the plane up. That plane is going nowhere fast. Kind of.

The only purpose the wheels serve here is to hold the plane up, and to eliminate most of the friction between the plane and the ground. When the engines fire up, the plane will still start moving forward. The only difference will be that the wheels are turning twice as fast as normal.

Please?!,
I Have been following your page for about a year, from when you first made it known that you were going Pro. And up until this I have had a pretty good feeling about your ability to reason. I have agreed and made movie choices after reading your reviews. But this is a very difficult thing for me to read. If the plane while still on the ground can not make forward progress it can not create the lift necessary to leave the ground. It uses the wheels roll in this way on take off. No matter how much force it can generate it can not leave the ground. Now if there is a major wind blowing at say 150 plus and depending on the size and weight of the plane, but this would have to be a air mass and consistency that would allow the plane to get far enough into the air, and then use the lift generated by the wing and engine. But hey if you pointed the plane stright up (Rocket) or say had the lift generating wing move(helecopter) you could solve the roll to forward speed thing that runways provide for. Because no matter how fast the air is moving through the engines the wind fmoving over and under the wing is the lift.

If prop thrust were enough to lift the plane up, then the wings would be no larger than the area behind the prop. Clearly, however, wings extend out much further than the props of plans. Consider also jets, which do not thrust any air at all on the wing, the thrust of a jet goes behind the wing.

Planes fly because there is more surface area on the top of the wing than on the bottom (the bottom is flat the top is curved). Because the air has to travel a greater distance over the top than on the bottom, the air gets spread out, as it were, and the air-pressure on the top of the wing is less than on the bottom. Because the air pressure is less, it generates upward lift.

It takes a whole lot of air moving at a rapid speed over a wing to generate lift. The props or jets aren’t going to move the plane forward because the plane is on a belt. If the plane is not moving forward, then there is no motion of air over the wings (and remember, the prop blast won’t cover the entire wing, so it is not enough). No air moving over the wings? No lift.

Just remember that the propulsion is relative to the air, and not the ground. Unless that conveyor belt can move the air above it at the same speed as the plane (but in the opposite direction), it’s not going to be stopping any takeoffs.

The question is broken, it seems to me. It says the speed of the belt matches that of the plane, whatever that means, but also implies that the plane is kept in its starting position.

When the plane starts rolling forward at 1 MPH, how fast does the conveyor belt move? 1 MPH the opposite direction? That means the wheels of the place are rolling at 2 MPH but the plane’s overall speed is not affected, except perhaps marginally by the added friction in the wheel bearings. The plane accelerates, and assuming the wheels can withstand moving at twice their normal maximum rate of rotation, it takes off.

But if you interpret the question as saying that the plane is somehow kept stationary by the conveyor, then of course there is no way the plane can take off, or move at all. However, if this is your assumption, then you had better be able to think of a mechanism by which the plane is kept stationary. I can’t imagine it.

The assumption that the plane never moves seems doubly flawed. Reading the question again, it would seem that while the plane is kept stationary, then the belt is also stationary (it moves at the same speed as the plane but in the opposite direction). So what is the purpose of the conveyor belt anyway?

Now,
After reading Cecil’s responce I now have a better understanding of the math problem. He states that if the plane is moving at 5 forward the wheels also move forward. ??? if the plane is mooving the belt is not keeping up the wheels hould only move in a backwards direction. If the belt is set to mach forward thrust. the wheels mach the belt’ speed. it is not twice the speed as stated in the 100 plus 100 = 200 example. It is 100 thrust matched by 100 belt = 100 wheels. which is still zero forward and zero lift.

The fallacy of your logic (as I see it at least), is that you’re forgetting something. The wheels of the airplane are connected to the plane, and friction exists between the runway (conveyor belt) and the wheels.

For the plane to take off, it has to reach a certain airspeed - the speed at which the air passing over the wing is enough to create lift. In order for the plane, which is on the ground, to reach a forward speed, its wheels would need to be travelling in a net forward direction. In order for this to happen, their speed would have to be GREATER than that of the belt running beneath them.

If, as the above indicates, the speeds are ALWAYS equal, then the plane will not move.

The point of the riddle is that the motion of the wheels exerts only a minor frictional force opposing the forward movement of the plane. The major force being supplied is from the plane engine, and that force is a forward force. The net force is equal to the forward force minus the negligible frictional force. This obviously produces a net forward force. Therefore, the plane moves forward, regardless of how much the wheels are spinning. The plane is not remaining stationary on the conveyor belt becasue there is a force acting on the plane that is not dependent on the motion of the conveyor belt.

This is really a fairly simple problem for anybody who has taken an introductory physics course, and I can’t believe that so many people are having such a difficult time with it.

The trick in Cecil’s question is that you read this sentence: “[t]his conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction)” and assumed that this meant that the plane is stationary with respect to a ground observer.

This is not the case.

The conveyor would have _no effect_ on the plane with respect to the ground observer. The wheels would spin madly, but no matter how fast the conveyor moved it would not slow the plane or send it backwards: the rotational velocity of the plane’s wheels only tell you what its speed is relative to the ground, not to the air around it. The jet engines are acting upon the air around the plane, not pushing against the ground.

In fact, since the conveyor belt would drag along a bit of air due to simple friction the plane would actually get into the air _quicker_ than if it was taking off from a normal runway. The conveyor moving in the opposite direction would drag a bit of air backwards with it, increasing the relative airspeed of the wing and increasing its lift (there may be some additional ground effect in play here that assists the takeoff as well…)

I have to agree with the people who are saying the the question is misleading. The plane will not in fact remain stationary.

Also, just for the record, the Bernoulli effect isn’t what makes planes fly! From the wikipedia article:

One common and incorrect way of understanding how an airfoil develops lift relies upon the pressure differential above and below a wing. In this model the pressures can be calculated by finding the velocities around the wing and using Bernoulli’s equation. However, this explanation often uses false information, such as the incorrect assumption that the two parcels of air which separate at the leading edge of a wing must meet again at the trailing edge, and the assumption that it is the difference in air speed that causes the changes in pressure.

Bryan, you’re neglecting the fact that the wheels (through the axle) are exerting only a minimal force on the plane itself. This friction is going to produce a small backward force, but not enough to cancel out the forward motion being created by the engine of the plane. Of course, we’re supposing that the system is near-ideal and that there is little friction between the axle and the plane. In a real case, the friction could be much greater, but theoretically the plane’s engines could still produce enough force to move the plane forward.

Let’s say for the sake of argument, that the engines on a jet propel it forward at 800 miles per hour (I have no idea how fast they really go, but bear with me here). Now imagine that the plane is sitting on a really long conveyor belt. Both the belt and the plane are stationary, and the jet engines are off. Now, imagine that the conveyor belt starts moving at 800 mph. Seeing that the plane’s engines are off, the plane gets dragged backward at 800 mph by the belt.

Now, if the pilot fires up those engines, that 800 mph of force is only going to counteract the backwards-moving conveyor belt, right? 800 mph in one direction less 800 mph in the other direction equals 0 mph. So, the plane sits stationary as the conveyor belt goes by beneath it.

If the plane isn’t moving, then the air isn’t moving above and beneath the wing at the required 800 mph, thus creating no lift. And that’s that.

On the other hand, if the conveyor belt could somehow drag the air along with it at 800 mph in the opposite direction of the plane, the jet propulsion would counteract the conveyor belt and the movement of the air itself would lift the plane off the ground… But that’s another story entirely.

The last of the idea of forward moving planes. If you look to the aircraft carrier. Would the navy have to use a catapult to get the planes into the air, no they could just hold them waiting for them to gain “forward thrust”. Planes don’t produce forward thrust they produce back thrust. if the belt was matching speeds the plane would not move.

The lift is created by the plane moving relative to the air around it (like you said)

But the conveyor is not moving the air around the plane. The plane is not moving in respect to the ground, the air (for simplicitys sake) is not moving irt the ground. The plane is moving irt the conveyor belt, but that doesn’t matter at all for the purposes of getting off the ground.

There is a serious problem with the wording of the question (and it’s discussed on the SD site). The terms “moving” and “speed” are not well-defined in the statement of the problem, and disagreement over the outcome can probably be traced back to differing interpretations of these terms.

If the plane is “moving” relative to stationary objects in the immediate environment (the ground, trees, buildings) then it is “moving” in a sense identical to any other plane during takeoff, and the outcome will be identical as well. If the plane is “moving” only relative to the conveyor belt (which requires a definition of “speed” that is questionable, in my view), then it’s behavior is identical to that of a stationary plane parked on the tarmac, and it will not take off.

Just remember that the propulsion is relative to the air, and not the ground. Unless that conveyor belt can move the air above it at the same speed as the plane (but in the opposite direction), it’s not going to be stopping any takeoffs.

I have to correct myself quickly, what I meant was:

Unless that conveyor belt can move the air above it at the same speed as the plane (and in the same direction), it’s not going to be stopping any takeoffs.

An observer standing stationary on the ground nearby would see this plane moving forward, at almost normal speed. The rolling conveyor is just ‘the rug being pulled out from under it’, and is barely slowing it down, right? If that’s the case, then this is a poorly worded question, giving the impression that the airplane is sitting still relative to a stationary observer.

Grey, you wrote “Now, imagine that the conveyor belt starts moving at 800 mph. Seeing that the plane’s engines are off, the plane gets dragged backward at 800 mph by the belt.” That’s not the case. This would in fact happen if we replaced the plane with a car that is “in gear” because the movement of the wheels is then able to produce a force on the car. However, an airplane’s wheels are nothing but free-spinning discs on axles. The backwards movement of the treadmill is going to spin the wheels, but these wheels will only exert a minor frictional force on the plane itself. Therefore, the plane will move backwards, but at a very small speed nowhere near the 800 MPH that the treadmill is moving. The case would be different if the brakes were engaged. Now the wheels would be supplying much more force to the plane, and it would move backwards at nearly the same speed as the treadmill.

If you don’t believe me, go try this out. Put a pair of rollerblades on and go stand on a running treadmill (you can hold on to the sides if you want). Your feet will move backwards due to some frictional force of the rollerblades’ axles, but they won’t move backwards at anywhere near the velocity of the treadmill. You’ll even find that you can pull yourself forwards with your arms (kind of like an airplane’s engine, huh?) Now, take the rollerblades off and stand on the treadmill in bare feet. I guarantee you that you’re going to be moving backwards a whole lot more quickly because now the force of the treadmill is acting on your body much more efficiently than it was when you were wearing the rollerblades.

Assuming ideal wheels, (infinite friction between the ground and the wheel surface, and no rotational friction between the wheel and its axle) if a conveyer belt started moving backwards, the planes inertia would keep it stationary. There is no force from the belt being put into the plane. If you add in the engine’s thrust, the plane would move forward at the same speed if the ground was stationary. Of course wheels are not ideal, but at real world speeds, its close enough to ignore the minimal friction.

I don’t think this is a really tough question, but as Kottke points out, having some beginning physics helps. Imagine the plane is on a completely frictionless surface (oil so slick, friction between the tires and the ground is absolutely zero). A car on that surface couldn’t budge. A plane, however, will move, since the force that propels it is independent of the ground. As a matter of fact, the wheels on the plane are acting just like a frictionless surface, allowing the planes propulsion (prop, jet, rubber bands, etc.) to create forward force. (where the lift comes from seems to be common knowledge amongst all the commentors here)

Same principle applies with the belt that equals the speed of the plane. The belt moves faster as the plane speeds up, resulting in the wheels spinning twice as fast (as compared to not have the belt/runway). Since the forward force (thrust, push, pull… it doesn’t matter in a force diagram) is independent of the ground, the plane takes off.

“That’s not the case. This would in fact happen if we replaced the plane with a car that is ‘in gear’ because the movement of the wheels is then able to produce a force on the car. However, an airplane’s wheels are nothing but free-spinning discs on axles.”

Okay, that’s fair, and I didn’t know that.

— Wait, before I go on: is that really true? On a jet? How does a jet taxi then? Isn’t there some sort of drive system involving the wheels? They don’t fire up the engines until they’re on the runway and cleared for takeoff, right? —

Okay, but, assuming that’s true of all planes, then it seems that that fact screws up the point of the question more than anything else. Suddenly it’s a question about planes and not a question about physics (which is a whole lot less interesting, if you ask me). I understand it to mean that the conveyor belt moves at whatever speed is required to counteract the forward motion of the plane. If that’s true, the plane doesn’t move at all relative to the ground and the air (even though it’s moving along at 1600 mph relative to the conveyor belt), and no lift is created.

Yeah grey, the wording of the question makes it a little awkward. I’ve seen it worded better in other versions. It is possible to read this version so that the backward movement of the treadmill is producing enough frictional force to counteract the foreward force of the engines.

As for your question about the wheels, I believe that most planes use their turbines or propellers for taxiing. That’s why you see those little cars pushing planes back from the gates. So the wheels aren’t connected to any kind of drive train.

Similar strangeness. Nearly Weightless Car in neutral on the same conveyor. You are standing next to the conveyor on stationary ground. You stretch out your hand and push the car forward a centimeter and stop moving. As you do, the conveyor goes backward. As it does, you keep your hand out, holding the car in place (1 cm from its original position), with just enough force to counter the reverse movement of the conveyor. If friction between the wheel and axle is 0, will the rpm of the wheels spin up to infinity if you keep holding the car in place?

Or what about: how fast are the plane’s wheels moving relative to the ground at takeoff if the takeoff speed is 60 knots and it takes 11 seconds to reach takeoff speed?

“It’s nice to see that there are still some people left in the world who have a basic understanding of physics.”

Wow. That is nice, there, Einstein. Thanks for honoring me with your presence.

“I agree the whole wheels thing is a red herring. A plane can take off from a frictionless surface.”

Okay, that’s fair, but the way I’m reading the question, it’s much worse than a frictionless surface. It’s a surface which is dragging the plane backwards at a speed equal to the force that’s pushing (or pulling, depending on the sort of plane) it forward.

“The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction).”

The conveyor moves at the same speed as the plane, regardless of what the wheels are doing. The wheels truly are a red herring, I think, because they aren’t meant to be part of the equation.

(I just quoted myself right there. What a loser.) Does it just blow your mind that a physics riddle could drive an internet conversation to this sort of snippiness? As much as I feel like I was right in reacting that way to that sort of condescension, I apologize to you guys for letting a conversation about something as inocuous as this bring that sort of snottiness out of me, no matter what anyone else said.

Having said that, if anyone brings up Hitler or the Nazis during this conversation, I’m throwing my monitor out the window. You have my word.

The conveyor is moving backwards at exactly the same speed of the plane, but that doesn’t mean that the backwards force is being transmitted to the plane. Again, the wheels have very little friction on the plane and therefore the plane can still move forwards with respect to the treadmill, even if the treadmill is moving backwards at the same speed. Because the wheels are freely spinning and have a minimal impact on the plane, you can essentially pretend that the plane is already floating in the air.

I just ran the question by a friend who is in grad school for Physics and he agreed that the plane would definitely take off.

The plane can not take off. To take off, the plane’s wings must reach a minimum speed relative to the surrounding air to generate the sufficient lift. Regardless of what’s happening on the ground, the wings are simply not generating lift (unless there happens to be a 180mph headwind on the ground).

The tricky part is that the limiting factor to a plane’s speed is usually the equalization of air resistance to engine thrust. If there’s no air resistance (because the plane is standing still) then the wheel resistance is the limiting factor. Since the rolling resistance of an airplane wheel is much less than the friction of wind on the body, the conveyor belt would likely have to be running at several times the speed of sound in order to generate rolling friction sufficient to match a jet under full engine thrust. Under those conditions the landing gear would likely melt or otherwise disintegrate.

Looked at another way, the energy being used by the jet engines should be equal to the energy that is being generated by the wheels, namely in the form of heat. Given that a commercial jet expends several gallons of fuel per minute those wheels would not be able to take the heat.

Of course, when the wheels break the jet will get pushed backwards at high speed when the body of the jet hits the conveyor belt. Too bad that the wind over the wings will be travelling in the wrong direction.

Also, as for my statement about people having a basic understanding of physics, I apologize for its negativity. It wasn’t really directed at anybody here, but rather was the product of some of the lame explanations that I’ve been reading around the internet these past few weeks. Again, I apologize if it offended anybody.

I don’t want to engage in snippiness, but better student than teacher. If the engine thrust and belt movement are zeroed there is now movement relative to the air and wing relationship. Credentials ( full thrust stall training at 5,000 feet) and planes do not float on air.

Derek, the wheels can freely spin as much as they want to along the treadmill. They’re exerting negligible force on the plane itself, so there can be a net forward movement if the plane’s engines produce enough thrust to overcome the backwards force.

“The conveyor is moving backwards at exactly the same speed of the plane, but that doesn’t mean that the backwards force is being transmitted to the plane. Again, the wheels have very little friction on the plane and therefore the plane can still move forwards with respect to the treadmill, even if the treadmill is moving backwards at the same speed. Because the wheels are freely spinning and have a minimal impact on the plane, you can essentially pretend that the plane is already floating in the air.”

See, that makes this a riddle about how the wheels on a plane work, not about physics.

“If the engine thrust and belt movement are zeroed there is [no] movement relative to the air and wing relationship.”

(I’m assuming you meant no ‘cause I thought you agreed with me here.) That’s what I mean. The belt is moving at whatever speed counteracts the movement of the plane, is the way I’m reading the question.

“See, that makes this a riddle about how the wheels on a plane work, not about physics.”

The brilliance of the riddle is that it combines the two. If you tried the same experiment on a car, there is no way that the car could move forward because a car relies on the contact of the wheels with the ground in order to gain its propulsion. A plane, on the other hand, can move forward without its wheels touching the ground. Therefore, if we assume that the wheels on the axle have minimum friction, they don’t effect how the plane moves forward.

“That’s what I mean. The belt is moving at whatever speed counteracts the movement of the plane, is the way I’m reading the question.”

The riddle doesn’t say that the speed of the conveyor counteracts the speed of the plane. Rather, it says that the speed of the conveyor equals the speed of the plane. In order for it to counteract the forward movement of the plane, the belt would have to transfer all of its backwards force into the body of the plane. However, because the wheels can spin freely, only a small fraction of the force is actually transferred, and therefore the plane can move forward.

Kevin, the wings are generating lift because the engines are pushing against the airmass in which the plane is located, not against the ground (no matter which direction it happens to be moving.)

A plane’s wheels can spin very quickly. When a plan lands those wheels go from zero mph to several hundred miles an hour of equivalent rotational velocity in an instant (which is why you see the puff of smoke on a landing as some rubber gets vaporized when the heat caused by the sort of friction necessary to spin up the wheels takes effect.)

Let’s imagine that the plane is taking off on a calm day. It turns on its engines and in a few seconds it is exterting the thrust that would normally move the plane forwards at 10mph. At this point the plane _is_ moving forwards at 10 mph (because it is pushing against a stationary airmass) and the wheels are spinning at a rotational speed that would measure 20 mph if you attached your car’s speedometer to these wheels; 10mph for the planes forward speed and 10mph due to backwards movement by the conveyor belt.

Please re-read the first paragraph of the problem and explain to me how this is not going to happen. The plane’s speed is 10 mph and the conveyor (which “tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction)”) speed is 10mph.

The plane still moves forward because it is not pushing against the ground and the wheels spin freely.

to kevin fox, and the folks who posted earlier and were also thinking that the original problem implies that the conveyor belt turns so fast that it’s keeping the plane stationary: no, it does not! absolutely no mention of that in the problem description.

to john: ni, in this context, your otherwise nice illustration does not make any sense, because the plane is not running on the ground in any way. that treadmill isn’t impacting its ability to move forward and generate uplift in any significant way.

if i may shoot down one more point: “In order for the plane, which is on the ground, to reach a forward speed, its wheels would need to be travelling in a net forward direction.” — Wrong!

“I don’t know how many of your are pilots, but that plane isn’t gonna lift off” — Jeremy, are you implying you’re a pilot? If so, I think your licence should be revoked at once. I’d be scared shitless if I found out I was on a plane piloted by you.

unless the wheels explode since they spin much faster than they are manufactured to do (atleast 2 times faster), the landing gear diggs into the conveyorbelt that breaks apart, pieces flying are sucked into the engines that fail, thrust is no longer generated and the massive increase of friction from the conveyorbelt against the broken landing gear starts affecting the airplanes speed…

And suddenly the conveyorbelt stops and the passengers can exit the aircraft…

And if the conveyorbelt reacts to the passengers I wish that all move either in opposite directions at equal speed or that they head for the side.

I may be misunderstanding this question, but the point of the conveyor belt is to maintain the plane in a single location relative to a stationary bystander? So I’m standing there watching the plane, and thanks to the conveyor belt it moves not an inch, relative to me. Right? If that is the case, then:

(a) the length of the conveyor belt is 100% irrelevant. If the wheels are stationary but spinning very quickly, the thing making them do that could be like two spinning rods like in a factory.

(b) the plane is not moving — the wheels are spinning madly but the plane itself is stationary. Therefore it can’t fly. If this scenario would work then they would forget the conveyor belt and just take off from a standing position in real airports. But they can’t do that, because a plane is not a helicopter.

Cecil says that planes fly by pulling themselves through the air. But if it’s standing still, how is it doing this exactly? Then why wouldn’t this work (to repeat myself) if the plane were turned on and standing on the runway? It wouldn’t, because a plane has to be moving through the air and letting air pass through and over it in some specific way.

I would also point out that the answers given thus far seem to be missing the element of time. If a conveyor belt plane (so to speak) will work, then would it work if the speed were very low and/or the time spent ramping up speed were very low? If not, why not? I submit that the process of working up to a “real,” from-the-plane’s-perspective speed of 800 mph or whatever is the same thing that ensures that the plane must be moving through the air from-the-plane’s-perspective to work.

The question does NOT state that the conveyor belt moves fast enough to negate any forward motion. It matches the forward speed of the plane, but in the opposite direction. That is, if the plane starts at X=0 and moves forward to X=100 feet, the portion of the conveyor belt that was originally at X=0 is now at X=-100 feet. The plane has gone 100 feet forward, the runway has gone 100 feet backwards, and the wheels have traveled over 200 feet of conveyor belt.

That’s the setup. The question is merely: can the plane move forward?

Ponder this:

1. The conveyor belt does not move backwards unless the plane moves forward. (You CANNOT dispute that… it’s in the definition of the problem.)
2. If the belt is moving backwards, the plane is moving forward. (Logically follows from #1.)
3. If the plane is moving forward, it has air moving over its wings and can take off. (From a rudimentary understanding of how flight works.)

Q.E.D.

I just solved it without using physics at all. The definition of the problem states that the plane can take off, because the only force that (in a small way) would counteract it only happens if the plane moves forward. If the plane can move forward, it can take off.

The reason a plane has wheels is to create what amounts to a frictionless take off surface. It merely needs to remain upright until it reaches a velocity where it can be supported by the air.

It’s true that _if_ the conveyor belt can zero the forward motion of the plane then the plane will not take off. However this would take a stupendously fast moving conveyor belt as it’s force is only being applied to the plane in negligible quantities due to the low friction between the wheels and the plane. This is a hard concept to grasp, but no less true.

The entire point of the question is to trick you into assuming the plane will be stationary. It wont be.

“I may be misunderstanding this question, but the point of the conveyor belt is to maintain the plane in a single location relative to a stationary bystander?” — Martin

Yes, you misunderstood. No, the plane is not kept stationary. If it was, your explanation would be entirely right, and it’s entirely reasonable to entertain that notion after reading through all the confusion above, but the original problem clearly says otherwise.

Also, ponder this: Lets imagine the conveyor was in fact moving extremely quickly because it tried to keep the plane stationary. I think it would move quite an amount of air along with it, throwing said air right at the plane. Now, this would make the plane take off even quicker.

lets take the big peed part of this out of the problem and think of the Alaskan bush pilot. If my Cessna needs 90 miles an hour to lift off, and I happen to be in a river at high melt that is traveling at 40 miles an hour, but I can only generate 120 miles an hour thrust, and I can only attempt a take off into the current can I get up. By the way there is no wind. It could be worse the wind could be blowing up the river, but that is a question for another time because I have to rush this liver to Anchorage. By the way the doner was mauled by a bear that can run at twenty miles and hour while he could only hop at two in his sleeping bag.

Inreresting perspective. So, if you were on a still lake, you could go 120 mph on it. But the water is moving at the unrealistic speed of 40 mph. How much does that slow you down? Surely not by a whole 40 mph. As you become faster, you’ll start rising out of the water and it’ll impact you even less. I’d say there’s no way it could prevent you from taking off. But if it did, at some point you’d have traveled several miles upstream; then you could just turn around and try in the opposite direction.

Plane’s engines propel it with a force that would normally cause it to go 300mph.

Thus, the plane’s wheels start to spin at the speed they would at 300mph.

Thus, the treadmill goes backward at 300mph.

Thus, the wheels spin at the speed they would at 600mph.

The plane doesn’t care how fast its wheels are spinning, since it’s basically just dragging them along frictionless. Instead, imagine the plane is simply magically hovering one spinning wheel’s height above the ground.

A plane’s jets or props are perfectly happy propelling it when it’s flying at 35,000 feet, and they’re perfectly happy propelling it when it’s flying one spinning wheel’s height above the ground.

The plane takes off.

And if you don’t believe me, the treadmill/rollerblades example above is the next best explanation.

As I taxi away from the dock live on Ice. the river pushes on me at an unrealistic 40 I turn up river I push my throttle forward. I come up to the dock generating enough thrust on the still lake to generate 40 mph but I am just staying equal to the dock the woman from the cafe hands me the coffee I forgot still with throttle generating 40 I now push it and get the engine to the max rpms which on the still lake would have given me a cool 120 but I am still not generating lift because the air relative to the wing not the engine is still only traveling at 120 minus the backward force of 40 which only gives me an air speed of 80 which is ten below my needs. the guy in Anchorage dies the guy in the sleeping bag died, and I tie my plane up and grab a burger because no matter how much I want my plane to fly physics will not let me into the air. and the jet at 30,000 feet is not on the ground an has attained enough forward speed to get where it is.

If you care to read my work , you will soon understand that the plane will not get off the ground. No matter how fast the wheels and propeller, and jet engine are going, the plane is not moving. And a stationary plane will not take off. Ever. Unless, it is the plane that Arnold was flying around at the end of True Lies. Or if there are tornado speed winds.

Derek, as to the lack of those 40 mph: It’s wrong to assume that the stream pushes everything submerged in it along at its full speed. The water flows around the pontons/floaters (what are they called? I’m not a native English speaker), they’re *designed* to let it flow around them with as little resistance as possible.

As to the 300—600 relationship: If the plane, compared to the stationary ground the conveyor is mounted on, goes 300 mph in one direction, and the surface below it (the moving conveyor belt) goes 300 mph in exactly the opposite direction, then from the point of view of the plane, the conveyor belt is moving at 600 mph. Thus, its wheels spin as quickly as if … etc. Simple, right?

“I just solved it without using physics at all. The definition of the problem states that the plane can take off, because the only force that (in a small way) would counteract it only happens if the plane moves forward. If the plane can move forward, it can take off.”

The thing that people are interpreting differently is relative to what the plane is moving forward. If it’s moving forward relative to the air, then you’re right. If it’s moving forward relative to the conveyor belt, then you aren’t (unless it’s moving forward relative to the air as well).

“The way the wheels of a plane work _is_ physics. :)”

No, it’s mechanics (and trivia, if you ask me).

“The entire point of the question is to trick you into assuming the plane will be stationary.”

“No, the plane is not kept stationary … the original problem clearly says otherwise.”

First, I think it’s pretty clear at this point that it certainly doesn’t clearly say otherwise.

And I don’t think it’s tricking us into assuming anything. I think we’re assuming it because what the hell’s the point of the question otherwise? If the plane can move forward, then of course it can take off. If the “trick” to knowing the answer here is knowing whether or not the wheels on a plane spin freely, then it’s a terribly uninteresting riddle, no?

o.k.
if the plane generates enough force to move at 300 and the conveyor belt matches that 300 the wheels need only 300 to keep up. the wheels themselves are not driven. so they can only be acted on by ether force generated by plane or belt. Each of which is 300.

If the plane can move forward, then of course it can take off. If the “trick” to knowing the answer here is knowing whether or not the wheels on a plane spin freely, then it’s a terribly uninteresting riddle, no?

Jason, I’m sorry for spamming your wonderful blog with so many comments, but … I can’t resist … I simply must point out to Bernoulli once again that the plane is not stationary. If it was, the conveyor belt would also be at rest and thus act like any other runway. Also — again this is redundant, others have pointed it out already — it’s wrong to credit the uplift that makes planes work solely to the Bernoulli effect. If a Concorde, for example, redlied only on the Bernoulli effect to take off, it wouldn’t be much more than an extraordinarily big paper-weight.

In the first stage, the jet engines are exactly equivalent to the motor of a car - they propel the vehicle forwards. But the diffrence is that a plane has wings which create lift and the plane takes off.

If the car had wings, or indeed was capable of getting airbourne it would only do so once it had achieved enough foward motion for the air passing over the wings to create lift.

In a simlar way, if the plane had a gigantic internal motor that drove the wheels (much like a car), and could reach a fast enough speed, it too would take off.

Of course once this plane was in the air (or the car with wings for that matter) it would fall back to the ground as it’s method of propulsion effectively ceases.

With the second stage of flight - the propulsion from the engines pushes the air backwards and the plane forwards, creates enough foward motion for the wings to maintain their lift affect.

The pupose of wheels on a plane is to create a frictionless environment BUT only so that it can move forward.

Think of a dragster, as it spins on grease and remains stationary - at this point there is no danger of it taking off. But as it propels down the track and reaches a significant speed, a malfunction may sometimes cause it to lift off.

nex,
the numbers were round. the point was that if a force conveyor( I could even spell conveyor before this talk) or river works against a grounded plane. it has to over come that force to get enough air speed for flight. I am also aware that a bear does not have to run after a guy in a sleeping bag. fish in a barrel, or their term campers in a tent.

I guess my point is that if planes could lift off from conveyors. Everyone would be doing it. The Advantages of a short runway are enormous. In the most critical cases, carriers at sea, a catapault is used to move the plane faster relative to the air (the ground is not relevant) in order to get it airborne. If the plane is stationary in relation to the air, I don’t think it will take off.

If a particular plane needed 40,000lb of thrust to travel at 300mph and somebody put it on a conveyor belt running backwards at 300mph, how much thrust would you need to keep the plane stationary? In reality I could probably hold it still with my pinky finger*

Sure, the wheels would be spinning at 300mph, but I’d be holding the plane still with very little effort. If somebody then turned on the engines and applied 40,000lb of forward thrust, the plane would obviously start moving forward and ultimately reach something very close to 300mph.

Hence, YES the plane would clearly take off in the given example.

* Okay so the pinky finger example might be a slight exaggeration, but you get the point ;)

beautiful,
Heliconia Summer photo. Yes pfong you are right the capault is used to generate forward force to get a plane into the air. and yes Hongknog and many other places would have conveyors if it were that simple.

Derek, imagine an aircraft carrier moving through the ocean at 10 mph (8.7 knots). Imagine you are on the flight deck of said carrier, jogging 10 mph in exactly the same direction. Assuming you use the full length of the deck, you half a little over half a minute, before you fall off the end, to think about this: How fast are you moving with respect to the ocean? Yes, you are only running at 10 mph as far as your feet are concerned. Yes, the carrier only moves 10 mph, too. However, this is where we introduce the mysterious concept of *addition*.

And might I add, defensively, to grey: “The plane moves in one direction […] tunes the speed of the conveyer to be exactly the same (but in the opposite direction).” — original problem. It’s clear that the speed of the plane is not measured with respect to the conveyor, because if it was, the speed of the conveyor would *always* be the same as the plane, but in the opposite direction. (It would be impossible to find out which speed to *tune* it to.) Thus, it’s clear that the plane isn’t stationary.

The plane will take off, because there is no way the conveyor could make it remain stationary.

The question is posed in a way that leads one to assume that the plane would somehow remain stationary by means of the conveyer moving in the opposite direction. This assumption is wrong. The plane will move forward and take off regardless of how fast its wheels are turning (which is the only effect the conveyor has).

not mysterious at all. If I am running a ten and the boat is at ten in the “same” direction then relative to the water I am traveling at ten plus ten and over a given time say one half minute I would have traveled ten plus ten at time rate of on half minute which would put me at the end of the boat or wet in your example. the distance traveled relative to the water would be more as two forces propelling me forward. But if I travel ten in the opposite direction than the boat my time to end is decreased, beause the boat moves under my feet when I am in the air, my strides then can be longer, but my relation to the water is equal. That is the theory of relativity.

Derek… The conveyor belt could be running at 2000mph, it’s still only going to take 40,000lb of thrust to get my plane to 300mph. I could also still (theoretically) hold the plane stationary with my pinky finger - no matter what speed the conveyor belt was moving. Sure the wheels would be spinning faster, but there would be very little extra backwards force to counteract.

pfong - Nobody is saying the take-off distance will be any shorter. This conveyor belt would have to be the length of a normal runway.

nex, ya know, I read the passage you quoted and see it exactly the opposite way. To me, it seems that the speed of the plane has to be measured relative to the conveyor. Otherwise, like I said, the whole thing quickly degenerates into something much less interesting.

But, my point was that it clearly isn’t clear because all of these people are arguing, basically, about that one point of fact.

Derek, I only meant to say, if you have to equal speeds, they can still add up to twice that speed. This was just in reference to your question regarding the 300 + 300 == 600 example. If you are moving at 10 mph with respect to the ocean (soil) and the flight deck (conveyor) moves at 10 mph with respect to the ocean, but in the opposite direction, then your shoes (wheels) would move over the deck (conveyor) at 20 mph. 10 mph in opposite direction == -10 mph in the same direction, and difference between -10 and 10 is 20. I just simplified the problem to only involve addition :-) Also, it only involves demonstrative speed comparisons: Ship vs. water, runner vs. ship. In our new example, which is more analog to the original problem, however, you’re running 10 mph with respect to the ocean, but really 20 mph with respect to the deck. So yes, you’ll fall off sooner, BUT: If you just ran 10 mph, according to your pedometer, in one direction, turned around at the end, and then ran back at the same 10 mph, both durations would be the same. Here, the velocity of the ship is of no consequence.

The boat moves under your feet while you are in the air? No. Because: Before you jumped up into the air, you were standing at the boat. It imparted its velocity on you. If we ignore the effects of air friction (they aren’t so great anyway), you can jump up all you want, you’re still moving as fast as the boat, it won’t move under your feet. If that was true, you could travel around the earth just by jumping straight up and down, because, you see, the earth rotates beneath your feet[*].

________
[*] Offer void at North Pole and South Pole.

PS: Yes, I’m aware we’re basically of the same opinion, are both right, and just exploring the weirdness of relativity. But heck, it’s amusing.

grey, I think that’s exactly the point: Once you phrase the problem in a simple, understandable way, it’s so trivial, it’s not worth any amount of conversation. So if you define ‘clear’ to mean ‘instantaneously obvious to every reader’ … yes, you’re right, absolutely. I was thinking more along the lines of ‘it arguably means this-and-that, there isn’t so much ambiguity that the other position might also be valid’.

This reminds me of the problem with the bell boy and the three hotel guests who initially paid too much. The punch line being something like “but where did the other two dollars go?” Now, this question is actively misleading many people so much that they no longer are able to see the problem in an objective light, thus they don’t realize how trivial it is and will argue about it ad infinitum. However, what we’re dealing with here is just phrased a little awkwardly, it lacks this sinister quality ;-)

now,
I am confused and I said 100 would be my comment limit before sleep. I will have to get this straight or I will not sleep. the difference of ten miles per hour in one direction and ten in the opposite is 20. So in the gym when I am running on a treadmill and the speed indicator reads 3 miles per hour I am really putting out enough energy to be doing twice that. If I had ten apples and gave away ten apples I really gave away twenty. Or my real example while on rollers on my bike I am peddling and my speed reads twenty and the rollers are friction free and keeping up, they have to be traveling at forty to keep up with me. I’m still not there but I may be getting closer. If I am walking on a treadmill on an aircraft carrier facing towards the stern, and a guy is on a bike next to me on rollers but facing towards the bow we are not moving relative to each other, although he is riding at twenty and I am running at three. But if a dolphin swims by the boat from bow to stern and is traveling at three and the boat is traveling at eleven( because that is better than ten) the relative to each other their speed is 14. in fact relative to me and my biking buddy the dolphin is moving at 14, but if the dolphin is moving at three in the same direction then relative to the boat he is swimming at 8 in the opposite direction and the boat is moving at 8 relative to the dolphin.

Yes, that’s exactly it, with one exception: On a treadmill (simplifying just a bit), you can only be stationary with respect to the gym floor, because it’s too short to allow for movement forwards or backwards. So if the top half of the conveyor moves at 3 mph, the difference between 0 and 3 is 3, and the speed indicator reading is correct. You’re just keeping up with the belt, no need to put in twice the effort. If you removed the supporting structure, so the bottom half of the conveyor would land on the floor, the whole treadmill would move at 3 mph. Including its axles around which the belt spins. Now, the top half of the belt would suddenly move at 6 mph. After a while, this force would have been pretty much transferred to you, so now you’d really have to run at 6 mph to stay on the darned thing. But realistically, treadmills face a wall or a window, so long before that could happen, it would crash into said obstacle and cause blowenfuse with spitzensparken. Fun!

The plane can take off. Force exerted by the engine(s) pushes/pulls the air to make the plane go forward. The wheels simply roll. If the plane has a forward wind-speed of 100 mph and the belt is moving at 200 mph, the wheels may be spinning backwards at 100 mph but they are free-wheeling and don’t affect the forward movement of the plane.

Force exerted by the engine(s) only pushes the air, it doesn’t pull. If the plane has a forward wind-speed of 100 mph and you’d want its wheels to spin backwards at 100 mph, the belt would indeed have to move at 200 mph, but in the *same* direction as the plane. In the example at hand, it moves in the opposite direction.

Coming to that damn plane — it will take off. Since there is some confusion in the question and I must admit after reading some comments, for a brief moment even I JohnKerry-ied, but then I JKied again to my original position, that the plane will take off. The conveyor belt could be moving at 10 times the speed of the plane backward if it wanted(assuming that speed paradox is taken care of), the plane will still take off.

Think of it this way: if conveyor belt is stationary(your local airport), say, the plane moves at 300mph. It takes off. Good pilot. If conveyor belt is moving backwards in such a way that the plane appears stationary to a bystander, but the plane is still moving at a speed of 600mph relative to the belt (and it’s surrounding air). Infact, it might even be helped by such a conveyor belt due to whatever little extra air-current pushed back against its wings and hence will take off a second sooner than it would normally. I agree with others here, the treadmill-rollerblades example is the closest approximation.

I would like to see Jeremy Zawodny respond back, since he _IS_ a pilot, and he is disagreeing. I am surprised!

The plane takes off because of wind acting on the wings, not on the specific turbine part. You can do this experiment in any flight simulator. Have a Cesna parked and change the environment to very strong winds (80 mph if I am not mistaken… the stall speed for the Cesna). Let the parking breaks go and the plane simply lifts up, like a kite.

So I say the conveyor-plane would NOT take off for the reason Ricardo said in the 3rd comment: there would be no wind acting on the wings.

for god sake Derek Demarco, from the comment u had put into this discusion, i guest u’re not a mechanical engineer. So i’ll help you with some basic knowledge how an airplane and car can move forward:

1. plane can go forward, because the engine is pushing the air behind it.
2. Car can move forward, because the wheel “push” the ground.

please understand these simple principle first
—————————————————-
now, to make matter simple, let us imagine a swimming problem,

fictional fact:
Derek is a cyborg who had a wheel leg, he can swim but very affraid of drowning, so he went into children pool, in this pool derek’s wheel touch the bottom of the pool but his head is still above the water, so he can breath freely, the owner of the pool change the floor of the pool into some kind of waterproof conveyor belt (with the same speed control with the above topic).

assumption:
the conveyor only move the the floor but the water is not moving at all.
derek’s wheel can be changed into ‘freewheel” mode with no friction whatsoever

now:
if derek had to go from one side of the pool to other side, what will he do?this what derek will do:(s=second)

1s.
Derek: derek is still standing at the edge of the pool. and his wheel (remember that he is a cyborg with wheel legs) is always thouching the floor. also remember that derek now in “freewheel” mode, meaning that his wheel can rotate freely
conveyor: detected that derek’s body is not moving (0km/h)

1,5 s.
Derek: derek start using his hand to propel himself forward, his speed now 0.5 km/h
conveyor: detected that derek’s body is moving and now moving to other direction (0.5km/h)

2s.
derek: derek body start to have steady speed of 5km/h because he had a cyborg power hand to
conveyor: have the same speed with derek but with reverse direction (5km/h)

20s.
derek: derek now reach the other side
conveyor: stop moving

why derek can reach the destination even though the conveyor moving the other direction? because to move in water, we actually gain speed by our hand, so it doesnt matter if the floor is move.
by putting this principle into above topic, now we know that the plane can move just like usual.

now derek, can now u understand why the conveyor belt had nothing to with the plane movement?i hope u can now.

Someone just pointed me at this discussion and I thought I’d put my oar in…

Forget about speeds.

A object will move if a force is applied to it.

If the aircraft moves relative to the air (in a forward direction) and continues to accelerate (i.e. the force continues to act upon it), it will eventually reach its take off velocity and take off.

If the plane’s engines are generating x pounds of force on the plane, the conveyor belt has to exert an equal force to the plane, in the opposite direction to stop it accerelating.

The force that the conveyor belt can apply to the plane is due to friction in the bearings of the axles of the plane and between the tyres and the surface of the conveyor belt.

If the bearings and tyres are very very very inefficient, or the plane has its brakes on or is glued to the belt, i.e. coefficient of friction approaching 100%, then the conveyor belt has to be capable of counteracting the thrust of the plane’s engines to keep it stationary.
If it can do that, the plane remains stationary (and so does the belt).

Assuming the tyres and bearings are normally efficient i.e. CoF approaching 0%, then the force that the conveyor belt can exert on the plane will be much less than the force being applied to the plane and therefore the plane will accelerate and eventually take off.

Not frictionless, just that the force due to friction is less than the thrust of the engines…. as long as there is a positive force on the plane it will accelerate (ignoring friction due to air resistance)

I think this question would be better stated as: How much friction would there have to be so the plane could be prevented from taking off? Any real world wheel would cause so little friction that yes, the plane could still take off. But let’s say the friction is 90% (where 0% is no friction and 100% means plane glued to conveyor). What happens now? What exactly? Boggle, the mind doth.

It _is_ true that the engines push against the air and not the ground. However, while the wheels are on the ground, the conveyor belt _does_ have a “pulling back” effect on the plane.

Think about these perspectives:

(1) Imagine that the plane and the conveyor belt were both stationary, and the conveyor belt started moving backwards at a fixed speed. The plane would move backwards as well. If the engines were fired, the plane could accelerate to the point where it was no longer moving backwards. Right? The plane and the belt are at a balance under which the forward force of the plane (by pushing air back) perfectly counters the effect of the conveyor belt pulling back on the plane (by contacting the tires). There is some proportional relationship between the plane’s force and the belt’s speed. The belt doesn’t exert that much force on the plane because it only contacts it through the tires, which can spin. So the belt speed is probably some large multiple of the plane’s force: B=kP. So as long as B/P always equals k, I think, the plane can’t take off.

(2) Imagine the opposite. The plane is landing on the same conveyor belt. There is a speed at which the belt can move such (assuming that the plane can somehow get all of its wheels on the belt at the same time) that plane will appear to be stationary to an outside observer. Again, some relationship exists between the amount of force being put out by the plane’s engines and the speed at which the belt is spinning. If the plane reduces engine power and the belt reduces its speed — keeping this engine power:belt speed ratio intact — the plane and the belt can make adjustments in lock step so that the plane can eventually shut of its engines and the belt can stop moving at just the right time so that the plane will have never moved after both of its wheels were on the belt. Since it’s possible for this to happen without the plane taking back off, it stands to reason that the take-off scenario should be reciprocally _impossible_.

==> The real problem is this: The question supposes that there is _speed_ tracking in place, which isn’t right. The conveyor belt can be adjusted so that the plane never has _any_ speed. The real relationship that needs to be tracked is the relationship between the force exerted on the plane by the conveyor belt through its contact with the wheels and the force exerted by the engines by blowing air.

I think you’re right, pfong, Martyn answered that one succinctly and eloquently. However the conveyor would have to be sufficiently long, and of course the plane would have to carry enough fuel to keep it going for however long it takes to reach take-off speed. Just imagine a regular runway, a regular plane, but with the brakes applied. It would taxi very, very slowly to the end of the runway.

But if the wheels were frictionless, then none of the above would be true. The plane, engines off, would remain stationary, even if the conveyor belt started moving backwards. Then the plane could take off because no amount of convery belt speed could exert any force on the plane, and the wheels would just spin faster. Also, the plane wouldn’t be stationary if it landed on the conveyor belt, because the contact between the wheels and the plane wouldn’t have any slowing effect. However, as soon as the brakes were applied, the plane would slow much normally than it would on a stationary landing strip, because applying the breaks would interfere with the no friction assumption.

But the physical reality is that the conveyor belt would have some pull on the plane, though not much. It would have to move back _extremely_ fast in order to prevent the plane from taking off / keep it stationary when landing.

“So the belt speed is probably some large multiple of the plane’s force: B=kP.” — John

On one hand, you state that k is a simple multiplying factor. On the other hand, B is supposed to be a speed, and P is supposed to be a force. Thus, you don’t have an equation there, and there’s no straightforward way to resolve this.

Your other approach (hah!) is quite ingenious, but the conclusion doesn’t convince me. It’s supposed to be the same problem run backwards, right? So if the plane can successfully land and come to a stand still, the reverse would be a successful take-off. The fact that the plane wouldn’t take back off just reinforces this view.

Am I right that your last paragraph should be interpreted as: “The problem would have to be different in order to keep the plane stationary, but at it isn’t different, the plane will move and take off.” ?

“The plane will take off, because the conveyer belt can’t keep it stationary, no matter how fast it moves.”

Kottke should add this to his original post as it’s the most succinct and accurate explanation in this thread.

As has been stated several times, eventually the question isn’t one about airspeed, it’s about friction. Imagine the wheel is completely frictionless. In that situation you should be able to understand why the plane will take off. (Even if the belt moves at 100 Mph, it has no effect on the plane). In the real world, the wheels aren’t frictionless, but they are much closer to that than the other end of the spectrum. No matter what the speed of the plane, the effect of the conveyor belt is very small.

Really don’t understand why this is being debated. With no movement in the aircraft (as the belt keeps it stationary) then no air moves over or under the wings. Therefor no upwards air pressure or lift. The wheels of the aircraft serve no purpose other than to allow it to move AGAINST the air fast enough to achieve airspeed. If you had a steep, long enough incline you could slide a plane to airspeed. Wheels on a belt mean nothing, if the wheels were travelling at twice the speed of the belt it would mean the plane would be travelling at only half it’s required airspeed.

My typo rate is increasing dangerously. Maybe I should go to bed. But then, over here it’s 13:20. Will doesn’t think it’s a car, he stated that the wheels only serve the purpose of allowing the plane to move, which excludes the possibility of using them for propulsion. Well, that’s a start :-)

You’re standing at the start of a long treadmill wearing rollerblades, and I’m at the other end - but on the ground beyond the treadmill.

The treadmill is moving at 10mph backwards, but you’re holding on to the side, your wheels spinning at the same 10mph. That’s pretty easy right? Because you’re only having to overcome the friction in the wheel-bearings of the blades.

Now, we tie a long piece of rope around your waist, and the other end around mine and I start running away from you at a constant pace.

Of COURSE you’ll move forward. Because the force I’m exerting is stronger than the friction of the wheels on the rollerblades.

Doesn’t matter how fast the treadmill moves in the other direction, the only force I have to overcome is the friction inherent in your rollerblade wheel bearings.

And the propeller, or jet engine on the plane is pushing the plane’s mass not against the conveyor belt, but against the surrounding air.

The plane takes off. The wheels are passive, not active.

Now a road-car, where the force is applied directly through the wheels to the road, well that’s a different proposition entirely.

It does not take off. Imagine that it did take off. The second the plane left the ground, it would no longer be touching the conveyor belt. Now remove the conveyor belt from the scene since it is no longer interacting with our plane. You have a giant heavy plane, stationary, above the ground, with it’s engines going gangbusters. It’s like it’s taking off like a Hawker Harrier jet which it can’t do. It would hit the ground.

dino, once again I’m inclined to asked, why in the world would you assume that the plane is stationary? Why? Are you just pretending to assume this, without giving any explanation whatsoever, in order to make me go insane?

It wouldn’t take off. Lift is generated by air passing over the winds, even if the engine configuration was once that pushed air over the wings it would not be sufficient. The plane is remaining in a stationary spot, even if the engine is on 100% power.

Additionally, the conveyor belt is unlikely to keep up. I’ve seen comments suggesting this is why it would take off. Again, it won’t take off. Once the engine hits 100% and very little lift is being generated over the wings the aircraft will become unstable on the conveyor belt, hopping on and off the belt. Which will lead to at some point one wheel touching down before the other wheel(s) thus leading to a crash.

That plane isn’t taking off. The basics of aerodynamics make the possibility impossible if the aircraft is not moving forward at an adequate speed.

Oh, I just figured it out in my head. If the conveyor belt is going the opposite way to the move of the aircraft then it obviously will take off, and it will do so at ease.

The problem is trying to think outside the mindset of a human moving on a conveyor belt. Unlike humans, who can only move against the conveyor belt by moving one foot after the other, the aircraft’s wheels are constantly in contact with the belt, and the belt is moving in the same direction as if the plane was actually moving. So once the engine perks up and starts providing enough pull then I can imagine the aircraft will be able to gain sufficient speed.

The propellers are the propulsion, not the wheels. Seriously, people.
The conveyor belt can push as hard as it wants, and it won’t slow the plane down except a tiny bit for the friction in the wheels. The propellers will pull the plane through the air and it will gain enough speed to take off. Using the logic of you “no-fly” people, no plane should ever be able to fly, because as soon as it leaves the ground its wheels no longer have anything to push against. So it’ll fall out of the sky, right? In fact, we have just such a giant conveyor belt. It’s called the Earth. And it goes at 1669.79 K/h (at the equator) — using your (flawed) logic, a plane would have to have propellers powerful enough to shoot the plane at that speed (plus 200+ for the actual speed required to take off) in order to take off on a runway facing west. Since no engines can do that, you’d only be able to travel east (or at least, take off going east and turn around).

For the sake of a genuine discussion, will *anyone* claiming that the conveyor is holding the plane back by any significant amount care to explain *how* this is possible at all? Are all of those people just trolls? Or sock puppets of one and the same person?

Personally, I like to think that they are different persons and not trolling, but once they realize their mistake, which is inevitable if you try to explain the impossible and make any progress, they don’t dare to come back and admit their mistake. Cowards. But that’s just what I’d *like* to believe.

The plane is remaining in a stationary spot, even if the engine is on 100% power.

There is little to no correlation between the free spinning wheels of a plane and a plane’s speed. By the last few commentor logic, a plane should not be moving when it is in the air because its wheels aren’t moving. Think about the instant directly before and after a plane touches down. The wheels go from no rotation to many thousand RPMs within a second…what’s the difference in speed of the plane before and after that same second? very little. If there’s no connection between wheel speed and plane speed then, why do you guys think there is one when it is taking off (or any other time)?

This is absolutely ridiculous. I’m terrified that those of you that say the plane will fly are in positions of serious responsibility. FFS, look up the principles of flight. Under your logic we don’t need runways for takeoff, we could just hold on to the plane, wind up the engines and then let go. Ridiculous.

I get it now. Thanks for the thought trip. I enjoy thinking about stuff like this.

Another one I thought about recently - and couldn’t stop thinking about for days - is why Astronauts are weightless. I, stupidly, thought astronauts were weightless because they were in space and were somehow outside of the influence of Earth’s gravity. Duh… they’re weightless because they’re constantly falling to the earth and it’s their forward motion that causes them to keep missing the planet. I can’t believe that I wasn’t taught this - and how space objects orbit - at school. Or maybe I just wasn’t listening.

HM says:“This is absolutely ridiculous. I’m terrified that those of you that say the plane will fly are in positions of serious responsibility. FFS, look up the principles of flight. Under your logic we don’t need runways for takeoff, we could just hold on to the plane, wind up the engines and then let go. Ridiculous.”
You are absolutely ridiculous. I’m terrified that so many of you that say the plane won’t fly are silently assuming that it’s stationary. FFS, look up what the other side is saying. Under our logic, the plane is NOT stationary, but you just assume so and don’t every give any explanation whatsoever why this would happen. Ridiculous.

Okay, whether or not the plane can take off is a function of the conveyor belt.

If we assume a magic conveyor belt that can move at arbitrary speed to try and control the position of the plane it will *always* win and here is why:

Consider a 747 sitting at rest on this conveyor belt. It’s landing gear is supporting the mass and at rest on the still belt.

At time t = 0, the pilot fires the engines and releases the brakes to begin his take off rool.

At time t = 0+epsilon (where epsilon is a very small amount of time) the conveyor belt controller notices that the plane has started to move, and applies back travel to prevent the plane from moving. Of course the engines are applying tons of thrust against the air and the wheels are low drag so the conveyor belt can’t apply much force to prevent the plane from moving.

So the conveyor belt speeds up. Two things happen: 1) the bearings in the landing gear get hot. 2) the skin drag of the belt blows more air resisting the motion of the plane. At some conveyor velocity, probably around 1500mph, the bearings in the 747 landing gear will fail; the wheels will lock and the whole thing will be thrown of the back of the conveyor assembly.

Of course assuming an reasonable conveyor belt that human civilization can build; the plane won’t care and will just take of, suffering only a little extra bearing wear in the process.

The only way you’re going to keep the plane stationary on the conveyer belt is if you tie the fusalage of the aircraft down as well. Tightly.
If the the fusalage remains stationary, then the speed of the wheels would remain 0km/h. The conveyer belt would therefore have to run at -0km/h. As such, the plane will not take off.

If the fusalage is not tied down, the jet engines will move the aircraft forward. It does this by sucking air in, compressingen it and shooting it back out at much higher speeds creating thrust. (same principal as a high preasure hose, but using air instead of water).
At this point, the thrust will be high enough to move the plane forward but not to get the plane off the ground. That’s what the wheels are for, to keep the plane moving forward until it has reached takeoff velocity. The sensors on the conveyer belt will detect the aircraft moving forward, but no matter how much it speeds up in the negative direction, it has no effect on the movement of the fusalage. If the conveyer belt keeps speeding up, you will probably get a situation where the plane is moving forward while the wheels are actually moving in the opposite direction.

The plane will continue moving forward leaving the convayer belt behind it and will then take off once it has produced enough thrust.

Another way to keep the plane stationary is if all this is happening in a vacume. Without air, the jets wouldn’t be able thrust the aircraft forward let alone fly.

Even with a very long conveyer belt, it would not shorten the distance a plane needs travel before it has reached takeoff speed. (unless the conveyer belt is moving forward at high speeds and is connected to the fusalage, not just the wheels. In practice, a catapult is probably much more effective and it too is connected to the fusalage).

As a last note, based on the same principles, a plane shouldn’t have much problem taking off on ice.

The plane can only take off if it reaches the required air-speed ie. the speed of the plane relative to the air passing over its wings. As the plane is not moving relative to the air around it, only to the conveyor belt, it cannot achieve lift and cannot take off.

The plane takes off. Here’s an alternative version that makes this easier to see: assume, instead of the conveyor belt, that the runway is coated in grease. I’m talking cartoon grease here, the kind that completely eliminates friction. When the plane’s engines start up, they will push air toward the back of the plane and slide the plane through the grease. The wheels won’t turn because there’s no friction, but the plane will gain speed and take off.

What this version does is to subtract off the effect of the ground on the plane’s wheels. The conveyor belt version effectively subtracts off *twice* the effect of the ground on the wheels. Since the plane takes off from the grease, it takes off from the conveyor belt.

I can only imagine that people are picturing a plane sitting on a plane-sized conveyor belt something like a runner on a treadmill. PLEASE EVERYBODY, SAVE NEX THE ANGUISH… THE PLANE IS NOT STATIONARY! The plane is moving along a runway-length conveyor belt. Just the same way as you might push a rollerskate forward on a treadmill, the planes engines are pushing the plane forward down the conveyor belt. There is NOTHING to keep the plane stationary. It is not tied down. The brakes are not on. It is being pushed forward by the thrust from the engine(s). The conveyor belt is applying a TINY amount of backwards force on the plane, but that is all. Not enough to hold it stationary. Not enough to stop it reaching take-off speed.

Unless this is an F-22 or an F-15 with a thrust to weight ratio > 1 this baby isn’t getting any lift.

As mentioned above, lift is required to take off, and that lift is generated by the motion of the wing through air (or air over the wing). If the plan is rocketing away with it’s engines at full bore, but isn’t moving with respect to the wing, it isn’t moving.

The fallacy I keep seeing is that people think that the engines drive wind over the wings. That’s not correct, the engines propel SOME of the air through the turbine and out the back. This is not a lift generator (the sahpe of the wing creates a pressure differential which provides lift).

Picture it this way, a giant fan sitting in front of a stationary aircraft MAY cause it to produce lift. But a plane with engines rocketing but chained to the ground isn’t going to generate any lift. It’ll make a lot of wind out the back, but that’s all.

A plane’s engines don’t push air around the wings of the plane, they push the plane through the air.

To simplify the problem, let’s say that there was no conveyor belt and the plan had no wheels, just a flat bottom that rested on the ground. Assuming that the engines of the plane couldn’t overcome the coefficient of friction (no slippage) then now think if the plane would take off or not.

I give this answer: no ordinary plane. If the plane’s engines were so big that they created a kind of wind-tunnel effect, then yes, the plane could take off. But I don’t know of any plane’s that I think could do that.

Lou and Dan: the plane is not glued to the ground. “Let’s say that there was no conveyor belt and the plan had no wheels.” Oh, right. Or how about this: let’s say the conveyor belt was a farm and the plane was a pig.

“If the plan is rocketing away with it’s engines at full bore, but isn’t moving with respect to the wing, it isn’t moving.” You want the plane move with respect to the wings? Dude, that’s a helicopter.

Two consecutive postings that misspelled ‘plane’ in exactly the same way … suspicious.

JJ: hehehe … thanks for the sympathy. I’m not coming back because this is so terribly important, it’s just more interesting than the code I’m debugging on the other screen. It’s kind of fascinating how many different takes there are on the stationary plane theory. How many excellent, eloquent, logical explanations as to why a stationary plane cannot take off. And the absolute, total, overwhelming lack of a shadow of an explanation as to why the plane is supposed to be stationary. It’s like a very ugly accident with bits of brain splattered all over the place: it’s disgusting, but I just can’t stop looking. Maybe someone set up a Someone Else’s Problem field.

Call me paranoid, but having read the post by Your Grandmother, I’m convinced this is a troll. I wont feed it any longer. Jason, just in case you discover this mess and see that many posts by ostensibly different people come from the same IP, I suggest you delete them and my numerous replies with them.

But just in case someone else comes along and actually cares to read through some of the comments so far, just let me say this one last time: The plane is obviously moving. The problem description clearly states so. If you think this is wrong, prove it. If you can’t, you have no point.

The plane is clearly stationary because there are seven leprechauns to each wheel. As long as the Loch Ness Monster remains at the bottom of the loch, it cannot be seen by sonar, thus there is no lift. The tooth fairy, however, can push the plane as hard has he wants from behind, but because the conveyor matches the plane’s speed, his feet are also matched. Thus he cannot provide enough thrust to overcome the speed of the treadmill. So, in conclusion, due to ghosts, who are lighter than air, passing through the engines, not enough mass is expelled backward to propel the plane forward. And since ghosts leave ectoplasmic residue, it disturbs the surface area of the wings, which cannot generate enough lift to take off. Santa Claus.

“A plane is standing on a runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction). Can the plane take off?”

Let’s try and clear this up once and for all.

The plane will take off. And here’s why:

Let’s first make some assumptions.

1. The plane is on a runway (albeit one that can move), therefore the landing gear is extended.
2. The pilot will follow normal takeoff procedure, therefore the brakes on the wheels will be released, allowing the wheels to spin freely.
3. Takeoff speed for this plane is 300mph.
4. There is no wind.

“This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction).”

From this we can assertain that if the plane is stationary, so is the runway conveyer. The runway will only move if the plane does. This means that at no point can the runway go fast enough to keep the plane still, as the wheels will prevent it having any affect on the plane. Also, if the plane slows down, so does the runway. This also means that the speed of the plane relative to the runway will always be twice the speed of the plane relative to the surrounding air and nearby buildings.

The other thing to remember is that the planes propulsion acts on the surrounding air in order to propel the plane forward.

As the plane speeds up, so does the runway until the plane hits takeoff speed (300mph). At the same time the runway also hits takeoff speed (not that it takes off!) and at this point the planes speed relative to the runway is 2 times the takeoff speed, which would be 600mph and the wheels of the plane are spinning accordingly. The planes speed relative to the surrounding air (and the stationary control tower) is still 300mph.

Coming across your post I decided to take it to the experts. Seeing as I work for an Major Aviation Museum - I think we have the experts needed to answer.

1) In order for an aircraft to take off it needs air flow over the wings. You can spin the engines up as fast as you want - but if the aircraft is not moving relative to the air then no lift is produced. This is one reason that pilots like taking off (and landing) into the wind. They need less power from the engines to get the air flowing over the wings fast enough to produce lift (and we all know the more lift the better)

2) The Bernoulli effect is over-rated as the sole reason for flight. Most of the lift is produced by air flowing over the front (top) of the wing and being pushed down at the rear (top). A wing directs air down, causing lift (down-force). Bernoulli adds some lift to this effect but it is a joint effort - Bernoulli doesn’t answer eveything.

3) This is the really simplified version - or to put it another way - all that I managed to catch. Aerodynamics are not a simple as most think - and not as complicated as you would think… still it gives me a headache.

Therefore - if the plane is moving into to the air - and that air is flowing over the wing at the needed velocity, then yes, it will take off. If, as some think, the plane is not moving - it won’t take off. It’s all about the air flow… and whether you flap your arms hard enough….

As I understand it the speed of the plane is irrelevant, it’s the speed of the air passing over the wing that gives lift. So as the plane is relatively stationary to the surrounding air (there’d some air moving due to ground effect of a moving conveyor) it cannot lift. It can thrust all it wants, unless air travels over the wing nothing happens to give it lift.

I think people need to read the question a little closer. It’s not in any way confusing and at no point is it said (or implied) that the plane is stationary.

The plane can move, it’s just that the runway will move at the same time, at the same speed, only the opposite direction. The only consequence of this is that the planes wheels will have to spin twice as fast. Remember that it’s not the wheels that provide propulsion.

The plane won’t fly, but it has nothing to do with physics and everything to do with engineering.

First, you can’t build a conveyor belt that can support 910,000 pounds and move at 150 knots. Second, while the friction in the wheel bearings may be low, the friction between the tires and the conveyor belt will not be low - conveyor systems are generally made of sheets of rubber that sit on large diameter axles. If the axles are spaced far enough apart, they will act like wheel chocks, preventing the tires from rotating. If the tires don’t rotate, the plane goes with the conveyor belt. Third, the wheels are rated to operate at a speed from 0 to maybe 200 knots - the conveyor belt motion in the opposite direction would cause the wheels to turn at twice their rated speed, as well as the tires turning at twice their rated speed, generating twice the heat, not to mention operating on a non-flat conveyor belt surface. While the gear bearings might survive, the tires wouldn’t.

So if you could invent a conveyor belt that worked like concrete, and created special gear and tires that operated at twice their current design parameters - sure it would take off. Otherwise you’re going to get a nice fireball at the end of the conveyor belt.

Doesn’t the (oddly written) explanation of the cyborg in the pool above help, or am I nuts? If I’m standing on a conveyor belt in a pool while wearing roller skates (with excellent bearings, obviously), and the belt begins to move, I’ll begin to move in that direction, though at a slower pace than the belt, since I’m not a car with locked wheels. But if I then begin to propel myself through the water by swimming with my arms, am I not then creating enough force to move forward against the direction of the belt, no matter how fast the belt moves?

Obviously, I’m no physics expert or pilot, so be kind. I’m just askin’.

I am sorry if this has been answered already. I got about half way down before giving up …

All those arguing about LIFT and saying that a traditional plane can’t take off without air flowing over the wings at a (great) speed are CORRECT.
BUTThey are missing the point of this question (or riddle); the plane will take off in EXACTLY the same way a s a regular plane – by moving forwards very fast.
The conveyor belt is moving backwards at (for instance) 300mph but even if the plane’s jet engines were off the plane would remain stationary – the theoretically frictionless wheels would be spinning backwards at 300mph but the plane would stand still – imagine wearing frictionless rollerskates on a treadmill.
SOwhen the planes engines are on and providing enough thrust to propel the plane at 300mph, IT WILL MOVE FORWARDS AT 300mph and so take off, as normal.
It doesn’t take off while standing still.

Others have answered this question in a clearer manner but I thought I’d add one more voice of support.

Anyone heard of the Monty Hall Problem? or Monty hall paradox?
its not related to physics but its an interesting question.
read the below quote from the wikipedia article on the subject and try to figure out the answer for yourself before you read the entire article:

“The Monty Hall problem is a puzzle in game theory involving probability that is loosely based on the American game show Let’s Make a Deal. The name comes from the show’s host, Monty Hall. In this puzzle a player is shown three closed doors; behind one is a car, and behind each of the other two is a goat. The player is allowed to open one door, and will win whatever is behind the door. However, after the player selects a door but before opening it, the game host (who knows what’s behind the doors) must open another door, revealing a goat. The host then must offer the player an option to switch to the other closed door. Does switching improve the player’s chance of winning the car?”

What if we take the same plane, and suspend it just inches over the runway. If the wheels are moving fast enough to move the plane at the required 300 mph required for takeoff (assuming the wheels were touching the ground), and we suddenly _dropped_ the plane (stopped suspending it), would it fly, or would it drop the few inches to the runaway and shoot forward?

Paulski - If the *wheels* are moving fast enough? The wheels on a plane are not driving wheels, they don’t propel the plane forward, the jet engines or propeller engines do. The wheels are just on bearings so they can freewheel. Imagine the wheels on a bike when you stop pedaling.

Imaging the plane had skis instead of wheels, and the runway was made of ice or snow. The plane could still propel itself forward and takeoff because the engines propel the plane by pushing against the air.

Didn’t scroll thru more’n the first few responses cuz imo max hit it right off the top. It’s about the air rushing underneath the wings that gives a normal plane (ie. assuming no silly VTOL trick) its lift. The conveyor makes the plane essentially sit still.

This reminds me a little of the discussion we had in my physics class where we noted that the top of your tire has twice the instantaneous speed of your car and the point where your tire touches the road isn’t moving at all.

Ok, Danbee, point well taken. Not articulated well-enough on my part. Question still stands: If the engines are producing sufficent energy to propel the plane along the ground (were it touching) at 300 mph, would the plane lift off when no longer magically suspended, or would it drop the few inches to the ground?

OK, let’s say the plane takes off. When its wheels leave the conveyor belt, what is its airspeed? how fast is it going? how much air is moving over the wings?

The answer is, the airspeed is 0, and the amount of air moving over the wings is zero. So at that point, the plane, having no lift, lands once again on the magic conveyor belt. Which somehow, according to the daftness in this thread, makes it take off again.

Another question. What if the plane is a bus? Does the bus take off? When it takes off, what is its relative airspeed? How much air is moving over the bus’ wings? Oh, wait, buses don’t have wings.

So the thing which makes a plane take off is wings. Air moving over wings.

“This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same”

Speed relative to what? A) the ground or B) the conveyor belt?

A) then the plane will take off, since the conveyor just makes the wheels spin twice as fast, but does not slow the plane’s forward motion.

B) then the plane will not take off, and the conveyor will be spinning damn fast to exert enough backwards pressure via the rolling friction of the tires to hold the plane stationary (relative to the ground).

Anders Hoff:Imagine if you had a hundred doors, 99 with goats behind them and one with a car. You pick a door which you hope will reveal the car.
The game host then goes on to open 98 doors revealing goats behind them.
This leaves you with two doors. The one you chose and one that might hold the car too.
Personally, I would switch doors if I was given the choice.

Same with three doors though the chance of getting the car is a lot less then when having 100 doors at your disposal.

Mark Jaquith is right on this question. Just read the prompt of the question carefully:

“The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction).”

Therefore, if the plane is moving at X, the conveyer will be moving at -X. Given that the PLANE IS MOVING, the wheels must be spinning at 2X.

Could a plane take off if the friction of the wheels happened to be twice the normal amount? Probably, because they don’t produce all that much friction. Most of the friction is from the air.

No where in the question does it claim that the plane remains stationary.

So imagine you’re on a bicycle on a convayer belt with rockets attached to it.
You start pedling, and the tires attempt to propel you forward, but the opposite motion of the convayer belt will keep you stationary. This is how a car or bus would react to a convayer belt.
You then let go of the peddles and launch the rockets on your bicycles. Not the tires, but the rockets pushing the air behind it away will propel you forward and there is nothing the convayer belt can do about it. Your tires are spinning independantly at that moment. You move forward and this is how a plane would react to it.

So the next question is: if you peddling your bicycle on a convayer belt while staying stationary, can you keep your balance?

I think the confusion here is that BOTH answers (fly/not fly) are possible, depending on the mechanics of the airplane’s wheels. On reading the problem initially, most people see it as ultimately suggesting (if the plane actually takes off) that we could have ridiculously shorter runways, but:

Given: the frictionless, passivity of airplane wheels (they’re not doing the propelling), and
Given: that the plane WILL NOT remain stationary (the force of the engines will propel it forward DESPITE the speed of the conveyor, be it 10 or 10,000,000 mph),

the runway will still have to be the typical length, because the plane will have to cover the same amount of distance to achieve its takeoff speed (moved forward that distance by its engines). And it WILL take off.

NOW! for a moment consider that we alter the function of a plane’s wheels and make them active, make them not turn freely against the motion of the conveyor, make them like the wheels on a car… could the plane ever fly then? The answer is NO, because the plane’s wings will never get the lift they need from the movement of the air around them.

if the tracking system keeps the conveyor belt running at the exact opposite speed of the plane, then if the plane starts out stationary (the assumption here, I think) then it will remain so. when the engines fire, creating forward thrust, the conveyor belt will compensate, keeping the plane stationary, with its wheels spinning backward.

So: the plane remains stationary.

So: there’s no air moving over the plane’s wings

So: the plane stays on the ground.

Things which would take off:

Helicopter
Crow
Hot air balloon

These things provide lift without airspeed. Fixed wing planes do not, no matter how powerful their forward engines are, nor if they have jet, rocket, or ion drives.

The obvious answer is the answer here. The conveyor belt with its compensation system is confusing.

If you want to make a conveyor belt make a plane fly, remove the plane’s wheels, and reverse the speed of the conveyor belt and allow it to move the plane forward. The plane will fly in the same manner that your hand makes a paper airplane fly.

The plane will take off because the plane will move forward (relative to the observer) under this scenario. The runway is moving at 300 mph backwards, the plane is moving 300 mph (relative to the ground) forward and 600 mph (the speed of the wheels passive rotation) relative to the runway (at the point of take off). The plane’s thrust will move it forward regardless of how fast the belt is going because of the spinning of the wheels.

When a plane is on the ground, it’s propellor or prop produces thrust that has nothing to do with the ground, rather, it is thrust against or pulling of, air. The ground provides minimal resistance due to the ability of the wheels to spin freely.

If the plane is stationary to the ground, by the definition of the riddle, so would be the conveyor.

that would be the same. there is also an example of something like that in the article at wikipedia.
with a hundred doors the chance of winning would be even greater if you switched doors at the end(when the host had opened the other 98). or am i wrong?

and as for the plane; it would fly. i liked alan’s rug explanation. that made me understand it.

The plane’s engines push against the air, so the plane moves forward no matter what the conveyor belt does. It is true that its wheels would be turning a lot faster backwards, but the plane would still move forward, because it makes thrust regardless of the conveyor belt.

This thread says more about the ability to people to talk past each other without listening than it does about planes and physics problems.

Much of the source of confusion here is that people conflate force with velocity, and have incorrect perceptions around how the wheels on a plane function.

The plane rolls forward basd on the force produced by its engines, as always. The ground provides upwards force, as always, until the airflow over the wings produces enough force to lift the plane. From a distance, it would look exactly the same as a normal takeoff, except the wheels would be spinning twice as fast as normal. If you want, you can make the treadmill run twice as fast as the plane is moving forward. It makes no difference.

Also, Jason, whether it makes it to the end of the belt is irrelevant — I think for most academic examples they’d assume the belt is endlessly long to remove that issue.

The people who think the plane won’t take off are simply assuming that the plane will not move forward, which is completely incorrect. Even a simple car placed on the conveyor belt would be able to move foforward, simply by spinning its wheels twice as fast. The car’s speedometer would show 60 MPH, but it would be moving forwards at 30 MPH relative to whatever object the belt sits on top of and the belt would move backwards at 30 MPH in the reverse direction. Don’t assume that simply because they are linked to move in opposite direction at the same velocity they have to cancel each other out — the whole point of wheels is to unlink one axis of movement between two objects.

Part of the problem here is the use of text rather than diagrams. Drawn on a blackboard, this problem would not challenge the average freshman physics class.

By now everyone should understand why the plane would be able to take off. I just thought I would give another example as to why. Imagine a car with two pontoons sticking out of its doors, keeping it afloat on a lake. Next to the car is a small airplane with two pontoons sticking out of it’s fusalage keeping it afloat on the lake. Now, start the car and floor it, the wheels simply spin in the water not moving the car anywhere (maybe just slightly forward). Now start the airplane engine and floor it. The plane moves forward, dragging it’s wheel through the water, and evntually takes off. The water and pontoon are the same frictionless surface as the wheels and conveyor belt.

for u who cannot imagine a basic prinsipal about jet engine push the air, i give u simpler problem.
let us imagine a swimming problem,

fictional fact:
Steve jones is a cyborg who had a wheel leg, he can swim but very affraid of drowning, so he went into children pool, in this pool Steve jones’s wheel touch the bottom of the pool but his head is still above the water, so he can breath freely, the owner of the pool change the floor of the pool into some kind of waterproof conveyor belt (with the same speed control with the above topic).

assumption:
the conveyor only move the the floor but the water is not moving at all.
Steve jones’s wheel can be changed into ‘freewheel” mode with no friction whatsoever

now:
if Steve jones had to go from one side of the pool to other side, what will he do?this what Steve jones will do:(s=second)

1s.
Steve jones: Steve jones is still standing at the edge of the pool. and his wheel (remember that he is a cyborg with wheel legs) is always thouching the floor. also remember that Steve jones now in “freewheel” mode, meaning that his wheel can rotate freely
conveyor: detected that Steve jones’s body is not moving (0km/h)

1,5 s.
Steve jones: Steve jones start using his hand to propel himself forward, his speed now 0.5 km/h
conveyor: detected that Steve jones’s body is moving and now moving to other direction (0.5km/h)

2s.
Steve jones: Steve jones body start to have steady speed of 5km/h because he had a cyborg power hand to propel himself
conveyor: have the same speed with derek but with reverse direction (5km/h)

20s.
Steve jones: Steve jones now reach the other side
conveyor: stop moving

why Steve jones can reach the destination even though the conveyor moving the other direction? because to move in water, we actually gain speed by our hand, so it doesnt matter if the floor is move.
by putting this principle into above topic, now we know that the plane can move just like usual.

now Steve jones, can now u understand why the conveyor belt had nothing to with the plane movement?i hope u can now.

Well, I don’t know if this has been proposed but the only way of the plane taking off in this situation is if the conveyor was instantly shut off providing the plane with an enormous amount of forward momentum near instantly. This would not be a vertical take-off but a drastically shorter runway/conveyor could be used than the traditional length. Following that theory could a plane land on a shorter runway that was moving at a speed relative to the plane, a virtual flypaper scenario?

“Much of the source of confusion here is that people conflate force with velocity, and have incorrect perceptions around how the wheels on a plane function. ”

Exactly, I’ve read tons of comments in which people think that simply because the conveyor belt is moving backwards with the same velocity as the plane is going forward, the plane is going to remain stationary on the belt. They fail to recognize that the backwards force on the plane is the minimal force of friction, becasue the wheels are spinning freely on an axis. The speed of the belt has little nothing to do with the motion of the plane. If we’re assuming a negligible frictional force, we can easily imagine that the plane is sitting on a bed of air above the belt (like in air hockey). The belt can move backwards as much as it wants, it’s going to have no effect on the plane.

“If this actually works, then why aren’t aircraft carriers built smaller, with treadmill runways on the flight decks?”

You’re missing the point. The plane still needs the same amount of distance to take off, in fact maybe a little bit longer because of the slight backwards force acting on the wheels. The plane still needs to move forward enough to get up to x speed before its takeoff. However, it can do that regardless of what the treadmill is doing under it.

“Well, I don’t know if this has been proposed but the only way of the plane taking off in this situation is if the conveyor was instantly shut off providing the plane with an enormous amount of forward momentum near instantly.”

Actually, it wouldn’t provide anything of the sort. That’s kind of the point here — the belt has little or no effect on what the plane is doing. Stop it, start it, run it forwards and backwards — as long as it’s moving along the primary motion of axis (nose to tail) of the plane, it won’t affect things.

We do have a way of using a moving runway to shorten takeoffs. It’s called a steam catapult. But it works for the very reason this belt doesn’t — unlike wheels, it’s directly linked to transmit force to the plane along the axis of motion. If you tried to say connect the plane to the steam cat by placing its freewheeling front wheels on top of a platform driven by the cat, it wouldn’t work any more. The plane would just sit still and the cat would zip forward without transmitting any energy.

Just to clarify, a steam catapult is what they use on a modern aircraft carrier to assist aircraft takeoffs. It’s essentially a sled on a track in the deck connected to a system of steam-driven, pneumatic cylinders.

“Exactly, I’ve read tons of comments in which people think that simply because the conveyor belt is moving backwards with the same velocity as the plane is going forward, the plane is going to remain stationary on the belt.”

J, you’re overthinking this i think. Consider…

“This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction)”

The answer is in the purpose of this wrinkle. I don’t think it’s a trick question. Any physics profs in the house?

Actually it seems pretty sorted out now, so let me present you with another source of confusion: If that works, why don’t they do it on aircraft carriers? Well, actually, they do, sort of. As Tom K. said, a steam catapult is what they use on a modern aircraft carrier to assist aircraft takeoffs. But up to the moment when that catapult fires, the plane is actually held in place, so it can fire up its engines to full thrust, so they’ll provide maximum force once the take-off procedure starts for real. Of course, the key points here are that the lock is released when the catapult goes off and that it doesn’t really have anything to do with catapults or wheels.

Hmm, one thing that might not have been taken care of thoroughly enough yet:
alan taylor says:Here’s the point of confusion, imo: this sentence in the question:

“This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same”

Speed relative to what? A) the ground or B) the conveyor belt?

A) then the plane will take off, since the conveyor just makes the wheels spin twice as fast, but does not slow the plane’s forward motion.So far, quite right.

B) then the plane will not take off, and the conveyor will be spinning damn fast to exert enough backwards pressure via the rolling friction of the tires to hold the plane stationary (relative to the ground).No. First of all, you propose to tune the speed of the conveyor relative to the ground (and thus also to the plane, since you claim it’s stationary) to match the speed of (the plane, and since you claim it’s stationary, also) the ground relative to the conveyor belt. Once again: the speed of the belt relative to the ground should be carefully, skillfully, expertly, finely tuned to always be the exact speed of the belt relative to the ground. If the plane really remained stationary, *any* speed would fulfil this condition, so it isn’t a criterion at all. In this case, the speed of the belt is clearly undefined, thus saying it would have to be so-and-so fast is bonkers. And since we start from a standstill, this case is *always* the case. Option B just doesn’t exist at all. Option A is correct.

I have an engineering degree and teach physics at the high school level. The problem here is that the wheels can spin and spin and spin and have little effect on the motion of the plane. The plane *can* move relative to the belt because the wheels aren’t related to the motion fo the plane. The plane moves because the jets push air and according to Newton’s third the air pushes back.

The roller skate analogy someone used above works well. Let me restate it another way. Imagine that you stand on a conveyor on skates and hold onto a rope attached to a tree ahead of you. As you pull yourself forward via the rope, the conveyor spins to match the rotation of your wheels. So your wheels spin and the conveyor spins but you keep moving forward by pulling on the rope. The spinning of the wheels do nothing to move you forward. Other than a little friction, they do little to slow you down. The jets or props on a plane are pushing the plane, NOT the wheels.

This is nothing like the tetherball question or the three cylinders or the sprinkler-head. It’s just a very poorly worded question, with multiple interpretations, and that is why there is so much confusion.

You need to state what these speeds are relative to. I think there are 4 possible interpreations:

4) Plane with speed v wrt belt, belt with speed -v wrt plane. This tells us nothing about the plane’s speed relative to the ground - it’s just a tautology.

I guess the question is trying to get at whether situation (3) is physically possible. I.e., can the belt exert enough force on the plane to maintain it’s speed relative to the ground at zero? I’m skeptical, but it doesn’t it depend on how big the engine is, how much friction the wheels have, how powerful are the engines working the conveyor belt, etc.

Without any air moving over the wings to create lift, there will be no takeoff.

You’re making a simple problem way too difficult. Groundspeed is irrelevant. The airspeed is all a pilot cares about. There must be sufficient airspeed over the wing to generate lift. Jet engines do not make a plane takeoff. They simply move the wing fast enough to generate lift.

Now if you take that same situation and put a chain on the nose of the plane tied off a mile or so in the distance, like a giant kite, and set up a huge bank of fans that generated the necessary airflow over the wings (dependant on the craft, it’s weight and stall speed) then you’d see it lift off.

This can’t be compared to the three pistons problem or the tetherball problem. Those are clearly stated and have answers that can be proved easily. This is very, very poorly stated and has several different possible answers.

Philip
Cecil is correct.
Forget about the wind and lift for a moment. Can the plane move forward relative to the ground and air? The answer is yes. It moves forward because it has a big engine or big prop pushing against the air. The conveyor does nothing to change that. nothing. The conveyor only spins the wheels. You could in fact run the conveyor at any speed and the wheels turn relative to the conveyor but it doesn’t matter. Run them at 2x or 3x the speed of the plane. The wheels are free to spin but you still have some big-ass jet force pushing the plane forward.

I might be wrong, but it seems to me that the only difference between a plane moving on the conveyer belt and a plane revving it’s engines but keeping its brakes on (assuming the brakes could keep the plane from moving) is that, on the conveyer belt, the wheels will be spinning. And like everyone’s already said, spinning wheels don’t make lift, air moving (quickly) over and under the wings makes lift. I don’t think it can take off.

A similar situation would be at plane taking off with a very high tail wind. Let’s say the plane needs to be going 150 mph (in still air) to lift off. If that plane is taking off with a tail wind of 150 mph, I don’t think it’s going to go anywhere (since there will be in effect no air moving from front to back across its wings). Obviously, this would be hard to test outside of a lab, but that’s why you take off into the wind, right? So that you increase the speed of the air passing over the wings, without having to actually move the plane any faster.

Joe, case 3 does define the plane to be stationary, but there’s nothing the belt can do to keep it stationary. It’s rather like the mathematician who starved to death after he defined all those cans of food to be open. I don’t have the software handy to figure this out quickly and correctly, but I can show that the definition is absurd: If the plane speeds up by 10, its speed wrt belt is v + w and its speed wrt ground is w. What is the belt going to do about that, huh? Per your definition, it would have to speed up to -(v + w). But firstly, this won’t change the fact that plane wrt ground still moves at w, and secondly it will alter the plane’s speed wrt belt by -w, making it v + w - w == v. So let’s say it’s a really smart belt and it speeds up to -(v + w/2), making speed of plane wrt belt v + w - w/2 = v + w/2. Now the condition would indeed be fulfilled, but clearly the plane isn’t stationary. If there’s a flaw in my logic here, I’d be pleased to be corrected, as I said it’s absurd and I’m not going to think about this without a computer, it could give me a headache. But the question isn’t wheter it’s physically possible, the question is wheter it’s logically possible, and I think it isn’t.

I think he’s wrong. The wheels and engines are a means, not an end. The end is the amount of air moving over the wings, which give the plane its lift. You could have all the thrust and band-conveyer speed you want; if there isn’t, say, 170 knots of wind going over the wing—the WHOLE wing—the plane would not have enough lift to get up, much less stay up.

Has anyone thought about what happens once the plane takes off? We’ve got a plane moving at 0 mph relative to the ground. Let’s say it (miraculously) takes off. All of a sudden there’s a plane, what, two inches off the ground standing completely still (relative to the ground), with no air moving past its wings. I don’t think the engines exist to keep that plane in the air.

OMG, this thread is turning out to be a plane-wreck twice as much faster than all the ID-Darwin threads combined. Let’s simplify the problem, shall we?

Replace the plane with a special NatGeo designed Alaskan sledge; with its base shaped not like a ski, but like train wheels. Replace the conveyor belt with a sheet of ice-rails. Ofcourse we assume that this ice-rail won’t melt, no matter what the heat/friction. Instead of taking only dogs or only reindeers, take them half-and-half (you might want to keep them in two separate rows though. Some dogs can be bitchy if you keep them behind reindeers). Now let this bunch of overfed, sex-starved dogs and reindeers pull your sledge, while the ice-rails move backwards into the Pacific Ocean. Remember the dogs and reindeers are running on regular Alaskan ground, as they’d usually do, not on ice-rails. So they don’t experience the treadmill effect. Assuming you are a NatGeo expedition member, and you were to board such a sledge, starting from the west tip of Alaska and head eastwards, will you eventually reach Canada in the usual duration? Ofcourse you will.

Thus, we conclude that you moved. Relative to the ice-rails, relative to Alaska, relative to Timbuktu, relative to the moon, relative to SuitSat, but MOVE you DID. Hence the plane will move. Thus the wind will blow against its wings. Hencely by simple principles of aerodynamics lift will be created. Thusly the plane will takeoff.

As we can all *clearly* see the problem(riddle) is not whether the plane will move, but how many dogs and reindeers NatGeo will need?

Philip and Feaverish: Your claim that the airspeed is nought is bogus, since that simply isn’t anywhere in the problem description. Apparently there’s some magic word in that description that makes people unable to think properly (I guess I’m immune since I’m not a native English speaker *g*), so the bogus claim that airspeed == zero has been stated over and over and over ad nauseum, redundantly, again and again. It’s still not true; don’t let those fools sidetrack you.

The plane can only take off if it is moving relative to the air (this is how lift is generated). Therefore, the problem boils down to this: whether the conveyer belt can move the airplane - or not. This depends on the friction between the wheels and the airplane (since the wheels are not motorized). The frictional force F_f (given by F_n, the weight, times μ the frictional constant) must exceed the thrust force of the airplane’s engines. In any modern airplane built to fly, this frictional force would be nowhere near enough to stop the forward thrust of the engines.

nex: Here’s what’s confusing me — The conveyer belt is in a fixed position on the ground. The air (through which the plane has to move to create lift) is also in a fixed position relative to the conveyer belt. If the plane does have airspeed, then by definition it must be moving through the air, and thus it must be moving relative to the conveyer belt, right? That is, it must at some point run off the end of the conveyer belt (depending on the length of the conveyer belt, of course).

If the plane isn’t moving relative to the conveyer belt, then it’s not moving relative to the air — and it has to be moving relative to the air, or it has no airspeed, and therefore no lift. Right? What am I missing here?

First the problem only states that the conveyor belt is moving at same forward speed as the plane.

Thus if the forward speed of the plane is referenced to air speed then. IF the plane is moving forward at 5MPH (or any other velocity units) then conveyor is moving backwards at 5MPH referenced to air speed. Thus plane is moving with respect to air and lift will be acheived.

If the reference is to a building or ground. Then if plane is moving 5MPH forward then conveyor is moving 5MPH backwards. If we assume the air speed referenced to ground is zero. Then the plane has a forward velocity with respect to air and lift is acheived.

If the reference speed is to the conveyor belt then if the plan is moving 5MPH with respect to conveyor belt, then the belt must be moving opposite direction at 5MPH with respect to its self. Since the belt can not move 5mph with respect to its self it is an ill formed problem with the only soultion being the plane is not moving.

The thing to remeber is the wheels on the plane play no effect on lift.

Assuming the plane could take off and fly if there were no conveyor belt, the conveyor belt makes no difference at all. Really.

There is no power to the plane’s wheels, so contact with the ground is just to hold the thing up. A plane has wheels because skids (unless on water or snow) don’t work very well. Of course, other things work less well.

There is another aspect to the problem, as stated. If the conveyor belt is “smart” and always moves the same speed and opposite direction to the plane … if the plane is standing still relative to the ground, is the conveyor belt moving, at all? Of course, the forces that move the plane forward don’t depend on the ground (or the speed relative to the ground, for that matter). The relative ground speed of a plane taking off into a strong wind is measurably slower than the plane’s airspeed. That’s why they call it “airspeed”, because that’s what matters.

“If the plane is moving forward, there will be air moving over the wings
and providing some lift. It may seem counter intuitive, but the runway
moving in the opposite direction will actually provide more air movement
compared to if the run way were a conventional run way. There is some
friction between the air and the roadway. What happens is something
called a boundary layer is formed. One way you can think of this is the
gradient in car speeds as you move from the fast lane to the slow lane.
You can think of the fast lane dragging the slower cars along with
them…or conversely you can think of the slow lane slowing down the
faster cars. (As a car changes lanes, it affects the speed of the cars
in the lane it just changed into.0 The increase speed of the runway
under the plane tires will increase the frictional force on the airplane
(the rolling resistance friction in proportional to the speed of the
wheel rotation).?

Short answer, the plane will be able to take off when the airspeed over
the wings is enough to provide the lift to offset the gravity on the
plane. Watch birds on a really windy day, you will see that they
actually fly backward. The key is the airspeed, not the ground speed.”

This is really much simpler than you have all made it. While the wheels are on the ground, speed is relative only to the ground. So if the conveyor belt can really match the wheel speed perfectly, then the acceleration will always be 0, no matter how much force is generated. It’s no different than a CAR on a conveyor belt. None of the wings, thrust, lift, any other aerodynamic features come into effect until the thing has left the ground. As as long as speed relative to the ground is 0, it will never do that.

Rather than a magic conveyor belt, think about this case with a plane’s wheels on a magic completely frictionless surface. The plane can’t generate any forward velocity because the force is being perfectly matched.

Interpretation 1) The conveyor belt moves backward at the same speed as the plane is moving forward.

Since most of the backwards force produced by the conveyor is translated into rotational momentum at the wheels, the net impact on the plane is only due to the friction in the axles. This must be much smaller than the force exerted by the engines, so the plane can move forward. The engines would just have to work harder to reach take-off speed. Say the plane is moving at 1 mph. Then the belt moves at 1 mph in the other direction. This does not produce an equivalent force on the plane, but merely a lessor force. It just implies that the engines would have to do more work to get the plane moving 1 mph.

In this case, the backwards force produced by the conveyor would have to be massive… enough to produce friction in the axles equal to the force produced by the engines. If this were true, the two forces would produce torque and I imagine the plane would tip over! Or at least the wheels would break off… either way, the plane would probably burst into flames and not take off.

“None of the wings, thrust, lift, any other aerodynamic features come into effect until the thing has left the ground.”

That’s the thing. The ground has nothing to do with it.

“As as long as speed relative to the ground is 0, it will never do that.”

That’s the thing. The speed relative to the ground will not be zero for long, once you fire up those jet engines. Conveyor belt notwithstanding. The trick here is that it seems intuitive that if a conveyor belt is able to keep a “moving” car motionless, it will be able to do the same thing with a plane.

“Rather than a magic conveyor belt, think about this case with a plane’s wheels on a magic completely frictionless surface. The plane can’t generate any forward velocity because the force is being perfectly matched.”

This kind of proves the opposite point. If the surface is frictionless, where is the force coming from that matches the thrust of the jet engines? Friction with the ground is the source of a car’s thrust. Not so with a plane.

With a frictionless surface (like ice) a car cannot move forward. The car depends on the wheels (and friction) to move it forward.

A plane with a propeller or jet engine does not need the wheels (and friction) to move it forward. The propeller or jet engine can generate thrust without any help from the wheels. Thus, the wheels, in this case, would be spinning twice as fast as without the conveyor belt. But the plane does move forward and does take-off.

I’ll try to make it even simpler. Let’s say you’re sitting on the airplane and you can roll down the window and stick your hand outside. The engines are pulsing beneath you, and the conveyor is keeping up with the force the engines are creating (the friction is meaningless since you have a ‘smart’ conveyor that simply works hard enough to keep the plane’s relative position on the ground exactly the same as if it were parked) so that if you had set up a camera on a tripod pointed at your plane, the conveyor is keeping the plane in frame no matter how much thrust you apply. Now, you’ve stuck your hand outside the window. You will feel no wind pushing at your hand (like you would say in a car at 60 mph when you stick it out the window) and thus there is no airspeed. If you do not reach the airspeed necessary to generate lift then that plane is not going to take off, and airspeed of zero is certainly not enough.

Oh boy, so much new text while I figured out that problem for joe. Didn’t read it all yet, but in reply to
Feaverish:
Wrt you, the riddle can be considered solved, congratulations! You see, the assumption that the air does not move relative to the conveyor belt is silly. If this was the case, you would be right. But how could a simple conveyor belt cause all the air above and around it to move as if it was glued to it? How would you glue, bolt or screw the air on? You can’t. But for the sake of your argument, let’s assume you can, and we immediately run into the next problem: You say that as the plane moves relative to the belt, it must fall off at the end. This is also wrong, because the belt is an endless loop, it has no end. The runway which it comprises has an end, but so has every ordinary runway, too. Doesn’t prevent planes from taking off. Long story short meaning: Your thoughts weren’t making any sense to begin with.

Joe, I found the flaw in your number 3:
3) Plane with speed v wrt belt, belt with speed -v wrt ground. Thus plane has speed 0 wrt groundThe conclusion is wrong. We have to consider: plane-belt, belt-ground and plane-ground. Which relationship between those holds invariably? Easy: Plane-belt + belt-ground == plane-ground, if you prefer to measure the belt-ground speed that way around. (Two possibilities, the underside of the belt turns in the opposite direction.) Now you stipulate that plane-belt shall equal belt-ground. Thus plane-belt + belt-ground == plane-ground == plane-belt + plane-belt == 2* plane-belt. Can the automatic conveyor control ensure that this relation is always satisfied? Yes, it can. It merely has to set belt-ground to plane-ground/2. Now, if you prefer to measure the belt-ground speed the other way around, the invariable condition becomes plane-belt - belt-ground == plane-ground, and you have to require that plane-belt shall equal -(belt-ground). What you did was switch the sign on on end of the problem and leave it be at the other end. This is when the math becomes incorrent and doesn’t make any sense, except in one case: when plane-ground == 0. But the fact that it falls apart in any other case doesn’t mean that there can’t be another case, it’s just plain wrong. I’m sorry for not being able to explain it better.

Philip, in reply to your last post: You just made up a nice problem that suits your ‘solution’. However, you were supposed to solve the *original* problem, which is entirely different, which becomes obvious once you care to actually read and understand it.

This thread is beginning to make me gravely concerned for the human race. I’ve never seen so many peverse answers to a relatively simple question in my life.

Last try:

1. The only significant unbalanced force on the plane is the thrust of the plane.
2. The speed of the belt is irrelevant. None of its velocity will translate into any significant force on the plane.
3. The plane moves forward as normal and takes off.

Someone made a joke earlier about the plane levitating 3 feet over the belt. For all intents and purposes, that’s the right way to think about this — the only force you get from the landing gear is the one counteracting gravity. The belt’s motion does not affect the velocity of the plane in any way.

Bruno - your analogy is great, and simple. I challenge you to actually physically perform the experiment - I’ll wager that you’ll be surprised as your board-yanking will not in fact keep your matchbox car stationary.

Trampas, your assumption that there can be a solution to an ill formed problem is … uh … creative. But props for figuring out that some definitions of plane speed persented here are nonsense.

Paul says:Rather than a magic conveyor belt, think about this case with a plane’s wheels on a magic completely frictionless surface. The plane can’t generate any forward velocity because the force is being perfectly matched.The force of the plane’s forward thrust is completely countered by a magic thing that is completely frictionless and thus utterly incapable of exerting any force on it? In case you have a driver’s licence, I demand you destroy it at once.

My comment regarding John Pritchard’s “Interpretation 2) The conveyor belt moves backwards fast enough to keep the plane from moving forward at all.”: Finally someone worded this interpretation intelligently, thank you very much, but it’s not a valid interpretation. The problem clearly, unambiguously states: Conveyor speed equals plane speed. At no point does it even hint at the shadow of a possibility that the conveyor could be moving at whatever speed it takes to make that plane burst into flames. Interpretation 2 is simply wrong.

chris says:my god…
you guys really are living upto some stereotypes here…And you, Sir, are leaving an impression that defies every stereotype known to mankind so far. Your assumption that the aeroplane has no engine of its own is asinine. Yet you talk down to us from your high horse … oh, wait, there *is* a stereotype you’re fitting … well I better won’t say what it is, I don’t want to be that rude.

Bruno, it is not the same experiment. In order to make it analogous, you first would have to blow on the pen, then you would have to watch how fast the pen moves, with respect to the room, not the notebook, and move the notebook at equal speed into the opposite direction. So why in the world would the pen remain stationary? There is nothing to dispute, the burden of proof rests with you alone. Good luck.

Bruno, here’s a suggestion for you: Use more all-caps sentences. Use more exclamation marks. Use more bold mark-up. Repeat the same argument more often. Make up more differently-looking, but essentially identical arguments, and repeat those, too. After a while you’ll be the only one left arguing and can walk away with the wonderful impression that you were right all along.

No retrades… your original thought experiment was correct in its construction, and I do applaud the fact that this discussion has at least now focused on the right issue — does the vehicle move, not issues of lift or airflow.

The car with a balloon was the right analogy. Unfortunately, the results of that experiment don’t support your hypothesis.

Bruno, I was just making fun, no bad intent. You are right that the notebook *can* compensate for the movement of the pen, but this has nothing to do with the problem at hand. To act analogous to said problem, you would, as I already said, have to move the notebook at a very specific speed, not however violently you have to in order to hold the pen back. The magic conveyor belt that cancels out the airplane’s velocity is nowhere to be found in the original question. And I’m FUCKING sick of pointing that out every 30 minutes for another dork, mkaythx.

If the plane guns its jets, it will be forced forward in the air, **dragging its wheels behind it**. If the wheels are touching a conveyor belt which is going in the opposite direction, the wheels will spin faster than normal, but the plane will take off.

And, I repeat:
This problem will be much easier in a few years, when they replace that ancient “wheel” technology with magnetic levitation. “Imagine a plane floating three feet above a conveyor belt…” ;-)

If I blow after the pen, if it is a balloon propeled car or a jet, wouldn’t the movement be compensated by the surfice it is on top?

Let’s ignore the pen (it’s not tremendously analogous to the original problem) and concentrate on the car. All that matters is the forces on the car:

1. forward force from the jet of air being shot out of the baloon.
2. backwards force from any resistance created by the friction inherent in the axis of the wheels.

Assuming that (2) is low enough that the car could move forward without the moving surface beneath, it is highly unlikely that you could ever move the surfact fast enough backwards to create the force necessary to cancel (1).

In fact, I’d suggest that (2) is so small that if you put the car on a table with a sheet of paper under it, and yank the paper out quickly directly along the axis of travel of the car, you’ll find the car hardly moves at all — the sheer momentum and air resistance of the car alone will overwhelm the force created by the moving surface underneath its wheels.

But if the plane is over the conveyor belt - stationary - how can the air speed rise to make any significant air pressure change on the wings? ”

You’re adding that concept that the plane is stationary. It’s not in the problem at all. The plane will move forward and take off, with air flowing over the wings in the normal fashion. Its wheels will just rotate faster to compensate for the backwards motion of the belt.

“What you dispute, then, is if the fact of the conveyor belt go in the opposite direction - tuning the speed - will be enough to make the airplane stay stationary or not?”
Err, no, I *know* that the force of the conveyor belt will not be enough. If the belt could counter all of the movement of the plane, the plane would not move, thus the belt wouldn’t move either, thus it would be exactly like any ordinary runway. You’re basically trying to prove that planes can’t take off from ordinary runways. Yes, on the conveyor, the wheels will have to turn twice as fast. Factor of two, no more. You think that is a problem? Prove it.

To the moron who posed this poorly worded question in the first place:

If you’re up in the control tower watching this plane, is it moving down the conveyor belt or not? In more simple terms: Is it doing what every other plane that you cleared on non-belted runways is doing?

If it is, it’s going to fly.

If it’s still putzing around, engines gunned, the conveyor working overtime, then it’s going nowhere.

If the car goes forward one turn - or X - and the surface goes backward an exact X distance, Why would not the car be stationary?The surface is absolutely not defined to go backwards the exact same distance as that covered by the plane’s wheels on the surface. This would be impossible to do in the context of the given example. Rather, the surface is defined to go backwards the exact same distance as the plane covers with respect to the ground.

I just remembered something I learned while doing math problems with fellow students: Don’t work on the solution for a problem with people who haven’t undestood the problem yet. Don’t work on the solution yourself until you know you have undestood the problem. If you don’t know what you have understood so far, hope that it’s just because you’re drunk or tired, and will be resolved after a good night’s sleep.

You’re right. If you’ve ever been in an airplane, you know when it takes off that what the wheels are doing doesn’t really matter. They help you to taxi down the runway, but when the plane is going to take off, the pilot starts the engines.

Once the jet engine is going, it is sending a huge amount of material very quickly behind it, and in order for momentum to be conserved, the plane _must_ move forward. It’s not a question of whether the jets are pushing on the air or not (if that were the case, thrusters wouldn’t work in space), but whether the jet fuel is causing a change in momentum. If they are, and they are in this case, then by the laws of physics, the plane must move forward, at which point the aforementioned Bernoulli principle will allow the plane to take off.

The problem with the question is, it implies that the plane will remain stationary. If the plane is anything like planes we have now (i.e., they are propelled by jets or a propellor rather than accellerating wheels), then this is simply impossible.

This question has a very obvious answer if you stop using your intuition and start using basic physics. There are three horizontal forces acting on the plane:

1. The thrust from the engines. For simplicity, let’s say this force is constant - surely we can all agree that the engine thrust is independent of any conveyor belts on the ground.

2. Friction from the wheels touching the belt. If the belt is moving, there will be some friction acting opposite the direction of motion of the plane.

3. Air resistance. If the plane is moving through the air, this force also acts opposite the direction of motion.

The question is, which is bigger - force number 1, or the sum of 2 and 3? It depends on the engine thrust, but if the plane is normally capable of accelerating to takeoff speed, then with the conyeyor belt we are only adding a little bit of extra wheel friction, so force number 1 is still larger, which means (via F = ma) that the plane accelerates in a forward direction and eventually reaches takeoff speed.

“If the car goes forward one turn - or X - and the surface goes backward an exact X distance, Why would not the car be stationary?”

You’re assuming that the surface is travelling backwards at X relative to a fixed point. That doesn’t necessarily follow from the relationship as you’ve defined it, or as the original problem did. The belt moves backwards at the _same_ speed that the plane moves forward.

The plane will move forward X/2, the belt backwards -X/2, in your definitions, relative to the static ground and air for each turn of the wheels. The speed of the vehicle is independent of this relationship and based on the force its engine produces.

“There will be no air resistance - from where I stand. : )
The conveyor belt would match the speed of the airplane, not allowing it to go forward. ”

Don’t you see - in deriving your answer, you are assuming the plane doesn’t move! Don’t assume anything, just do a simple accounting of forces and you arrive at the obvious answer.

I think what is tripping up a lot of people is that they can’t figure out how the plane gets started in the first place. The real difficulty there is that infinitesimal movements are not intuitive - that same difficulty is inherent in the classical Zeno’s paradox of Achilles and the Tortoise. But if you use the notions of calculus, i.e. F = ma, then the plane clearly moves forward through the air.

Ok I have not read many of the previous hundreds of posts but the answer is in the question itself.

If this magic conveyor belt is tracking the speed of the wheels on the plane and matching that speed, then the plane will sit in one spot just spinning its wheels.

HOWEVER, if this magic belt is actually tracking the movement of the plane through space and matching THAT, then the belt would just speed up and up causing the wheels to spin twice as fast, but the plane would still be traveling through space and eventually reach a speed that would cause lift.

Rehan, OK OK, you did figure out the solution. And if the originator of the question was super-duper intelligent, he wouldn’t have had to ask. There’s no doubt about it. I just think the question, as it is, is still good enough to have an unambiguously correct answer. It’s not hard to figure it out. Except for, apparently, a large fraction of average kottke.org readers. Are they morons? Or is it the fault of the question to Cecil? Hmmm … Well, anyway, I became a little aggressive with all this ignorance and unwillingness to think it through properly … I’m sorry.

Bruno, the plane can stand on a still surface, being stationary, right? It also can roll over the surface it’s standing on, right? So if you pull the surface away from under it, it can remain stationary, rolling over the surface, right? (Maybe you would need a little force to keep it in place, apart from its inertia, but the plane can provide that force with its engines, very easily.) So if it can remain in the same place, no matter what you do to the surface underneath, why is it hard to imagine that it can also move across said surface, no matter if it’s an ordinary, still one, or moving? It doesn’t matter. The surface the plane stands on doesn’t matter. Except for the small extent Nick explained. I find that if you know how a wheel works, it’s obvious that this extent must be small. If you don’t know how a wheel works, you should tackle that first before moving on to aircraft. I know I’m not helping much, but I’m not a teacher and to me the solution has always been obious, I can’t imagine to not see it, I can’t imagine how I would like to have it explained to me.

nex, I did read the question. There is one question posed: “Can the airplane take off?”

If the conveyor has “a control system that tracks the plane speed and tunes the speed of the conveyor to be exactly the same (but in the opposite direction)” then the plane cannot become airborne. If it does in fact have this “control system” so that for every 1 mph forward the plane would be traveling forward it compensates to bring it back to 0 mph forward, thus not allowing it to move forward from it’s starting position relative to everything else on the earth besides the conveyor upon which it rests, then it cannot move forward at all.

If it is not moving forward at all, then there is no air moving over the wings (which is the purpose of having a jet or a propeller attached to the thing) and it cannot take off.

I have not given the conveyor any magical properties - I simply read the problem as stated.

What people are getting tripped over are the jet engines. The jet is not causing the plane to fly. You would need a rocket (more thrust than mass) for that to occur.

Let’s take a glider. Ordinarily I need a crop duster to tow me at least 30 mph to get enough wind over my wings to get me airborne. A V8 engine and a cable can do it too. Let’s say twenty guys pushing really hard down the runway could do it, or twenty elephants or twenty whatevers. Put the lot of them on the conveyor behind my glider and have them shove. The conveyor keeps up with their pace so that they’re pushing me at 30 mph forward, ordinarily enough pace to get me airborne. However the conveyor is moving 30 mph in the opposite direction as stated in the problem.

You’re standing off to the side, arms crossed watching this whole fiasco unfold. The twenty guys are running like crazy, the conveyor is whirring along, the glider is bumping along at 30 mph over the ground - giving it a ground speed of 30 mph, a true ground speed of zero, and an airspeed of zero. I’m sitting in the glider looking at you and we still haven’t moved relative to each other. And my glider will never take off.

On the narrow point of my option 3, one of us is very confused, and I’m pretty sure it’s you. If you stipulate that the plane is moving with v wrt belt, and the belt is moving with -v wrt ground, the plane *must* be moving 0 wrt to ground. It’s just basic kinematics. It’s just the same as the following:

1. I am on a train, walking forward at 2 mph wrt the train.
2. The train is moving backward at 2 mph wrt ground.
3. Thus, i am stationary wrt to ground.

The question is whether you can physically achieve this state of affairs.

Tom,

I think you are totally correct that with any *realistic* friction force you can’t stop the plane from taking off. But if you postulate a strong friction force that *increases* as the relative speed increases, and if it increases fast enough, you should be able to stop the take off.

Dave,

By your reasoning, if you chained the plane to the ground and turned on it’s engines, the plane would start moving (wrt ground) no matter how strong the chains are. You are right that momentum must be conserved, but if the plane is chained to the ground, it is the plane & the earth that move forward.

With a normal plane and a super-normal conveyor belt runway (that’s how I’m reading the question), I believe that gravity would create enough friction to keep the plane stationary and that the propellers/jets would not generate enough airflow across the wings to produce any lift.

If this magic conveyor belt is tracking the speed of the wheels on the planeFirstly, it isn’t. It just isn’t. Says so in the problem description.
and matching that speed,Secondly, how do you define the speed of the wheels? You can’t be talking about the rotational velocity, since that has another dimension as the flat surface moving. So the straightforward definition of wheel speed is how much distance, per given amount of time, the wheel covers on the belt. And you want the belt move at the same speed …. in relation to what? The ground? Well, this would mean that to an observer standing on the belt, the plane would move forward about twice as fast. To an observer on the ground, it would move forward at about the same speed as on any other runway. So what?
then the plane will sit in one spot just spinning its wheels.As I just said, this doesn’t follow at all. Just because the wheels spin twice as fast, why in the world should that cause the plane to sit in one spot?

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Seriously, this discussion is making physics teachers roll over in their graves.

The belt is a red herring. It doesn’t affect the plane at all. It’s just distracting because most of us are used to thinking in terms of cars, where force for motion is generated via the wheels.

If the plane can’t take off, then how in the world can people do that trick where they pull the tablecloth off of a table and leave all the dishes in place?

The “no take off” crowd would be logically need to conclude that there is some magical force that keeps the dishes on the table, when in fact the real answer is simply that isn’t any force present that would make them move off the table (unless you have a really rough or sticky tablecloth).

And nex, I use the glider analogy to try to make it less open-ended. You seem to think the plane’s ability to move forward is limitless while the conveyor’s is somehow limited, thus the conveyer wouldn’t be able to keep up.

Nowhere in the problem was it stated what sort of propulsion the plane had. However, even assuming a jet engine, jet’s have limited force. The problem proposes that the conveyor is able to counteract the plane’s forward propulsion.

FOR BRUNO:
If u who cannot imagine a basic prinsipal about jet engine push the air, i give u simpler problem.
let us imagine a swimming problem,

fictional fact:
BRUNO is a cyborg who had a wheel leg, he can swim but very affraid of drowning, so he went into children pool, in this pool BRUNO’s wheel touch the bottom of the pool but his head is still above the water, so he can breath freely, the owner of the pool change the floor of the pool into some kind of waterproof conveyor belt (with the same speed control with the above topic).

assumption:
[1] the conveyor only move the the floor but the water is not moving at all.
[2] BRUNO’s wheel can be changed into ‘freewheel” mode with no friction whatsoever

now:
if BRUNO had to go from one side of the pool to other side, what will he do? this what BRUNO will do:

HE WILL MOVE HIS OWN BODY BY HIS HAND, THIS IS THE SAME WITH THE PRINCIPLE OF A JET ENGINE, CAN U GET IT? BRUNO THE CYBORG WILL EVENTUALLY CROSS TO THE OTHER SIDE OF THE POOL (EVEN THOUGH HIS CYBORG WHEEL IS TOUCHING THE FLOOR OF THE POOL)
THE ENERGY THAT BRUNO USED IS TRANFERS INTO THE WATER, NOT INTO THE FLOOR

if u can make the same analogy to the plane problem, then the movement of the conveyor is not an issue here!

Of course i can use some simple freebody diagram to be more scientific, but i guess u’re not a mechanical engineer right?

If the conyeyor belt wheels match the speed of the plane’s wheels perfectly, then the plane cannot move forward through the air.

If the thrust for the plane is coming from engines pushing against air (rather than through the tires like a car), the plane’s tires and the conveyor belt would rapidly speed up until one or both of them gave out. The plane would not move through the air, because it is still being held up by the ground, and that ground is moving away beneath it. That is completely different than a frictionless surface, which would make take off easy.

If the conveyor belt wheels spun 1mph faster than the plane’s wheels, the whole plane would drift backwards.

So in theory, the plane can’t take off.

In reality, the conveyor belt engine would quickly blow, the tires would skid and shred, and the plane would move forward.

“If you stipulate that the plane is moving with v wrt belt, and the belt is moving with -v wrt ground, the plane *must* be moving 0 wrt to ground. It’s just basic kinematics. “

Time to reread the original question. It says nothing of the sort. Don’t insert relationships that aren’t necessarily true.

“The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction).”

There’s no reason the plane’s motion is in any way tied to that of the belt. The plane has forces other than the belt working on it. In fact, it’s the belt’s speed that’s linked to the speed of the plane. You’re creating a relationship that isn’t stipulated by the original statement.

“The belt is a red herring. It doesn’t affect the plane at all. It’s just distracting because most of us are used to thinking in terms of cars, where force for motion is generated via the wheels.”

Tom, it’s mostly a red herring, but also a very badly worded question.

Let’s say that you’ve got a plane whose trust can propel it max 220 mph forward on a runway. Let’s make the (admitiddly unrealistic) postulate that the limiting factor here is the friction in the wheels, not air resistance or anything else. This means that it is the *speed relative to the runway* that is critical.

Then if you have the runway moving backwards (wrt the air) at 40 mph, you can’t take off. Similary, if there is a 40 mph tailwind, you can’t take off.

I think the above is correct, once you grant the wheel friction as the limiting factor.

It’s just the same as the following:
1. I am on a train, walking forward at 2 mph wrt the train.
2. The train is moving backward at 2 mph wrt ground.
3. Thus, i am stationary wrt to ground.No, Joe, no, it’s not the same, not at all. If you are *inside* a train, it’s like being in any other room. All the air inside the train, assuming the windows are shut, is pretty much still wrt the train, just like in any other room. So, you walk at 2 mph wrt the train, and because the train is moving into the other direction, your velocity is cancelled out, great. But what you fail to see is this: if the train gently accellerates to 3 mph, or breaks down to 1 mph, you won’t really notice much. You can remain stationary wrt the ground, as long as you coincidentally walk at the same speed, in the opposite direction. But what the velocity changes do NOT do is change your speed wrt the train, got that? Good.

But the plane isn’t inside a train. It isn’t standing on feet that have so much friction with the ground that as soon as they touch they ground, they move at the exact same velocity. In fact, the plane is anchored to the air, which, for the sake of this thought experiment, is stationary wrt to the ground. Not completely, if we account for the rolling friction of the wheels and axles, but surely it’s much more anchored to the (air above the) ground than to the conveyor. Now what happens is this: As soon as the conveyor changes its speed, the relative speed of the plane to the conveyor is changed. All your math is fucked now. That’s why the real math is more complicated and thus more confusing.

Pwb and Philip, you don’t qualify for looking for a solution because you obviously haven’t understood the problem yet. See above for an explanation. (Not necessarily in my posts, it’s even more obvious that I’m not good at explaining this.)